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1
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.
2
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.
3
Content available remote Multiple positive solutions to semipositone Dirichlet boundary value problems with singular dependent nonlinearities
Jiang D., Xu X., O'Regan D., Agarwal R. P.
Fasciculi Mathematici
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2004
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Nr 34
24-37
EN
In this paper we establish the existence of multiple positive solutions to semipositone Dirichlet boundary value problem by using the upper and lower solutions method with the existence theory in [1], where u > 0 is a constant. Here our nonlinearity/may be singular at y = 0.
4
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.
5
Content available On the number of positive solutions to a class of integral equations
Wang L., Yu W., Zhang L.
Control and Cybernetics
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2003
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Vol. 32, no 2
383-395
EN
By using the complete discrimination system for polynomials, we study the number of positive solutions in C[0,1] to the integral equation phi(x) = integral[...] k(x,y)phi^n(y)dy, where k(x,y) = phi1(x)phi1(y)+phi2(x)phi2(y),[phi]i(x) > 0,[phi]i(y) > 0,0 < x,y < 1,i = 1,2, are continuous functions on [0,1], n is a positive integer. We prove the following results: when n = 1, either there does not exist, or there exist infinitely many positive solutions in C[0,1]; when n [is greater than or equal] 2, there exist at least 1, at most n + 1 positive solutions in C[0,1]. Necessary and sufficient conditions are derived for the cases: 1) n = 1, there exist positive solutions; 2) n [is greater than or equal to] 2, there exist exactly m (m belongs to {1,2,..., n + 1}) positive solutions. Our results generalize the ones existing in the literature, and their usefulness is shown by examples.
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