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1
Content available Positive solutions to a third order nonlocal boundary value problem with a parameter
Szajnowska Gabriela, Zima Mirosława
Opuscula Mathematica
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2024
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Vol. 44, no. 2
267--283
EN
We present some sufficient conditions for the existence of positive solutions to a third order differential equation subject to nonlocal boundary conditions. Our approach is based on the Krasnosel’skiĭ-Guo fixed point theorem in cones and the properties of the Green’s function corresponding to the BVP under study. The main results are illustrated by suitable examples.
2
Content available Existence of positive continuous weak solutions for some semilinear elliptic eigenvalue problems
Zeddini Noureddine, Sari Rehab Saeed
Opuscula Mathematica
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2022
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Vol. 42, no. 3
489--519
EN
Let D be a bounded C1,1-domain in Rd, d ≥ 2. The aim of this article is twofold. The first goal is to give a new characterization of the Kato class of functions K(D) that was defined by N. Zeddini for d = 2 and by H. Mâagli and M. Zribi for d ≥ 3 and adapted to study some nonlinear elliptic problems in D. The second goal is to prove the existence of positive continuous weak solutions, having the global behavior of the associated homogeneous problem, for sufficiently small values of the nonnegative constants λ and μ to the following system Δu = λf(x, u, v), Δv = μg(x, u, v) in D, u = ϕ1 and v = ϕ2 on ∂D, where ϕ1 and ϕ2 are nontrivial nonnegative continuous functions on ∂D. The functions f and g are nonnegative and belong to a class of functions containing in particular all functions of the type f(x, u, v) = p(x)uαh1(v) and g(x, u, v) = q(x)h2(u)vβ with α ≥ 1, β ≥ 1, h1, h2 are continuous on [0,∞) and p, q are nonnegative functions in K(D).
3
Content available remote Positive solutions for fractional differential equation at resonance under integral boundary conditions
Wang Youyu, Huang Yue, Li Xianfei
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
238--253
EN
By using the theory of fixed point index and spectral theory of linear operators, we study the existence of positive solutions for Riemann-Liouville fractional differential equations at resonance. Our approach will provide some new ideas for the study of this kind of problem.
4
Positive and nontrivial solutions to a system of first-order impulsive nonlocal boundary value problems with sign changing nonlinearities
Hellal Meryem, Merzagui N.
Journal of Applied Analysis
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2020
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Vol. 26, nr 2
193--207
EN
In this work, we use the fixed-point theorem in double cones to study the existence of multiple positive solutions for an impulsive first-order differential system with integral boundary conditions, when the nonlinearities change sign.
5
Content available remote Positive solution for nonlinear fractional differential equation with integral boundary value condition
Zatla Y. T., Daudi-Merzagui N.
Fasciculi Mathematici
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2018
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Nr 61
163--177
EN
In this paper, we consider a fractional differential equation, with integral boundary conditions, when the nonlinearities are sign changing. Our approach is based on the Krasnoselskii theorem in double cones. We generalize some recent results.
6
Content available On the construction of two-sided approximations to positive solutions of some elliptic problem
Kolosova S., Lukhanin V.
ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
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2016
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Vol. 5, No 4
11--19
EN
In this paper we have investigated the existence, uniqueness and possibility of constructing of two-sided approximations to the positive solution of a heat conduction problem with two sources. The investigation is based on methods in operator equations theory in half-ordered spaces. In this case we have considered a nonlinear operator equation that corresponds to the initial boundary value problem in a cone of non-negative continous functions. The properties of the corresponding operator define conditions which provide the existence and uniqueness of the solution. The conditions link the parameters of the problem implicitly meaning that they don’t provide the range of allowed values but need to be verified for each specific parameters value set separately. During the investigation we have provided the scheme of a two-sided iteration process which must satisfy the conditions in order to converge to the positive solution from both sides. The computational experiment have been conducted in two domains – unit disk and unit half disk. We have applied both two-sided approximations method and Green’s quasifunction method for the problem solving. The obtained results are presented as a surface and level lines plots and also as a table. The results in corresponding domains obtained by different methods have been compared with each other.
7
Content available A note on the dependence of solutions on functional parameters for nonlinear Sturm-Liouville problems
Orpel A.
Opuscula Mathematica
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2014
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Vol. 34, no. 4
837--849
EN
We deal with the existence and the continuous dependence of solutions on functional parameters for boundary valued problems containing the Sturm-Liouville equation. We apply these result to prove the existence of at least one solution for a certain class of optimal control problems.
8
Content available Sobolev norm estimates of solutions for the sublinear Emden-Fowler equation
Kajikiya R.
Opuscula Mathematica
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2013
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Vol. 33, no. 4
713--723
EN
We study the sublinear Emden-Fowler equation in small domains. As the domain becomes smaller, so does any solution. We investigate the convergence rate of the Sobolev norm of solutions as the volume of the domain converges to zero. The result is obtained by estimating the first eigenvalue of the Laplacian with the help of the variational method.
9
Content available remote The boundary value problem of higher order differential equations with delay
He Z., Shen J.
Demonstratio Mathematica
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2013
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Vol. 46, nr 1
87--100
EN
In the paper, Guo–Krasnoselskii’s fixed point theorem is adapted to study the existence of positive solutions to a class of boundary value problems for higher order differential equations with delay. The sufficient conditions, which assure that the equation has one positive solution or two positive solutions, are derived. These conclusions generalize some existing ones.
10
Content available Positive solutions of arbitrary order nonlinear fractional differential equations with advanced arguments
Ntouyas S. K, Wang G., Zhang L.
Opuscula Mathematica
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2011
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Vol. 31, no. 3
433-442
EN
In this paper, we investigate the existence and uniqueness of positive solutions to arbitrary order nonlinear fractional differential equations with advanced arguments. By applying some known fixed point theorems, sufficient conditions for the existence and uniqueness of positive solutions are established.
11
Content available Right focal boundary value problems for difference equations
Henderson J., Liu X., Lyons J. W., Neugebauer J. T.
Opuscula Mathematica
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2010
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Vol. 30, no. 4
447-456
EN
An application is made of a new Avery et al. fixed point theorem of compression and expansion functional type in the spirit of the original fixed point work of Leggett and Williams, to obtain positive solutions of the second order right focal discrete boundary value problem. In the application of the fixed point theorem, neither the entire lower nor entire upper boundary is required to be mapped inward or outward. A nontrivial example is also provided.
12
Some applications of dominated convergence theorems to a higher order singular boundary value problem
Yao Q.
Journal of Applied Analysis
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2010
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Vol. 16, nr 1
15-30
EN
The existence of positive solution is considered for a singular higher-order boundary value problem, where the nonlinear term is a strong Carathéodory function. Two new existence theorems are proved by applying the Lebesgue dominated convergence theorem, the Fatou lemma and the Krasnosel'skii fixed point theorem of cone expansion or cone compression type.
13
Positive solutions for a class of nonresonant m-point boundary value problems
Feng M., Zhang X., Ge W.
Journal of Applied Analysis
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2008
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Vol. 14, nr 1
115-129
EN
This paper concerns the existence and multiplicite of positive solutions for a class of nonresonant m-point boundary-value problem of second-order diferential equations Lx = λw(t)(t, x), 0ρ -integrable for some 1≤ p ≤ +∞. the arguments are based upen fixed point theorems in a cone and Hoelder's inequqlity. The nonexistence of positive solution is also studied. In addistion, some examples are included to demonstrate the main results.
14
Content available Componentwise asymptotic stability and exponential stability of positive discrete-time linear systems with delays
Busłowicz M., Kaczorek T.
Pomiary Automatyka Kontrola
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2006
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R. 52, nr 7/8
31-33
EN
Definitions of the componentwise asymptotic stability and of the exponential stability are extended for positive discrete-time linear systems with delays. Necessary and sufficient conditions for the componentwise asymptotic stability and the exponential stability are established.
PL
Definicje asymptotycznej stabilności według składowych oraz stabilności wykładniczej rozszerzono na liniowe dodatnie układy dyskretne z opóźnieniami. Podano warunki konieczne i 90 starczające asympto-tycznej stabilności według składowych oraz stabilności wykładniczej.
15
Solutions of nonlinear singular boundary value problems
Sebai H.
Journal of Applied Analysis
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2005
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Vol. 11, nr 1
95-112
EN
We suty the existence of solutions to a class of problems u" + f(t,u)=0, u(0)=u(1)=0 where f(t, .) is allowed to be singular at t=0, t=1.
16
Content available remote On the recursive sequence Xn+1=alfa+Xn-k:f(Xn,....Xn-k+1)
Karakostas G., Stevic S.
Demonstratio Mathematica
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2005
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Vol. 38, nr 3
595-610
EN
The boundedness, global attractivity, oscillatory and asymptotic periodicity of the nonnegative solutions of the difference equation of the form Xn+l=alfa+Xn-k:f(Xn,....Xn-k+1, n=0, 1, ..... is investigated, where alfa > 0, k is an element of N and f : [0,infinity)- (0,infinity)k is a continuous function nondecreasing in each variable.
17
Content available remote Existence and nonexistence of positive solutions for nonlinear three-point boundary-value problems
Yuji L., Weigao G.
Fasciculi Mathematici
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2004
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Nr 34
157-167
EN
The authors study the existence and nonexistence of positive solutions to the three point boundary-values problem where 0 < Mi < 1 and Beta > 0, a > 0, A > 0. Different conditions for the problem (E) - (B) to hve at least one or two positive solutions and sufficient conditions for this problem to have no positive solutions are given, by applying a new Green's function of three point value problem.
18
Content available remote Positive solutions of initial value problems for singular integro-differential equations in Banach space
Liu Y., Qi A.
Demonstratio Mathematica
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2003
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Vol. 36, nr 4
847--858
EN
Global existence of positive solutions on [0,1] are established in Banach space for singular initial value problems of first order integro-differential equation of the form x'(t) = f(t, x(t), (Tx)(t)), t € (0,1), [ x(0) = 0, where f(t,x,y) can be singular at t = 0,1 and x = 0. Some applications for second order singular initial or boundary value problems are worked out.
19
Content available remote Boundedness and persistence of solutions of a nonlinear difference equation
Stević S.
Demonstratio Mathematica
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2003
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Vol. 36, nr 1
99--104
EN
In this paper we obtain sufficient conditions for the boundedness as well ;is for the unboundedness of the positive solutions of the difference equation xn+1=f(xn,...,xn-k+1), n=0,1,2,...,where k is a positive integer and the initial conditions x-k+1, X-k+2,...x0 are arbitrary positive numbers.
20
Content available remote Global continua of positive solutions for some boundary value problem
Huy N. B., Thanh T. D.
Demonstratio Mathematica
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2002
|
Vol. 35, nr 2
303-311
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