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1
Content available Forced oscillation and asymptotic behavior of solutions of linear differential equations of second order
Shoukaku Yutaka
Opuscula Mathematica
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2022
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Vol. 42, no. 6
867--885
EN
The paper deals with the second order nonhomogeneous linear differential equation (p(t)y′(t))′ + q(t)y(t) = f(t), which is oscillatory under the assumption that p(t) and q(t) are positive, continuously differentiable and monotone functions on [0,∞). Throughout this paper we shall use pairs of quadratic forms, which obtained by different methods than Kusano and Yoshida. This form will lead to a property of qualitative behavior, including amplitudes and slopes, of oscillatory solutions of the above equation. In addition, we will discuss the existence of three types (moderately bounded, small, large) of oscillatory solutions, which are based on results due to Kusano and Yoshida.
2
Content available remote An abstract nonlocal functional-differential second order evolution Cauchy problem
Bednarz A., Byszewski L.
Technical Transactions
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2018
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Vol. 115, iss. 4
139--147
EN
The aim of the paper is to prove two theorems on the existence and uniqueness of mild and classical solutions of a semilinear functional-differential evolution second order equation together with nonlocal initial conditions. The theory of strongly continuous cosine families of linear operators in a Banach space is applied. The paper is based on publications [1–12] and is a generalization of paper [7].
PL
W artykule udowodniono dwa twierdzenia o istnieniu i jednoznaczności całkowych i klasycznych rozwiązań semiliniowego funkcjonalno-różniczkowego zagadnienia ewolucyjnego Cauchy’ego rzędu drugiego z nielokalnymi warunkami początkowymi. W tym celu zastosowano teorię rodziny cosinus liniowych operatorów w przestrzeni Banacha. Artykuł bazuje na publikacjach [1–12] i jest uogólnieniem publikacji [7].
3
Content available Second order inferencje in natural language semantics
Pulman S.
Journal of Language Modelling
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2018
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Vol. 6, No. 1
1--40
EN
In this paper I look at a number of apparently trivial valid inferences (as well as some invalid and missing inferences) associated with the possessive construction and with different types of adjectival modification of nouns. In the case of possessives, all analyses I know of, whether implemented or not, systematically sanction invalid inferences. In the case of adjectives, there are some model-theoretic linguistic analyses that are adequate at a theoretical level, but no satisfactory practical computational implementations that I am aware of which capture the correct inference patterns. A common thread between the possessive and the adjectival construction is that to derive the correct inferences we need secondo order quantification. This is an uncontroversial move within modeltheoretic formal semantics but a problem for computational semantics, since we have no fully automated theorem provers for anything Rother than first order logic (and only for subsets of first order logic do we have provers that are both fully decidable and efficient). I explore what is needed to provide a proof-theoretic account of the relevant inference patterns, and suggest some analyses requiring second order axioms. In order to make this a practical computational possibility I go on to propose two techniques for approximating such inferences in a first order setting. The suggested analyses have been fully implemented, and in an appendix I provide a small FraCaS-like corpus of relevant examples, all of which are handled correctly by the implementation.
4
Content available remote An abstract nonlocal functional-differential second order evolution problem
Byszewski L.
Technical Transactions
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2017
|
Vol. 1(114)
147--154
EN
The aim of the paper is to prove two theorems on the existence and uniqueness of mild and classical solutions of a semilinear functional-differential evolution second order equation together with nonlocal conditions. The theory of strongly continuous cosine families of linear operators in a Banach space is applied. The paper is based on publications [1–9] and is a generalization of paper [6].
PL
W artykule udowodniono dwa twierdzenia o istnieniu i jednoznaczności całkowych i klasycznych rozwiązań semiliniowego funkcjonalno-różniczkowego zagadnienia ewolucyjnego rzędu drugiego z warunkami nielokalnymi. W tym celu zastosowano teorię rodziny cosinus liniowych operatorów w przestrzeni Banacha. Artykuł bazuje na publikacjach [1–9] i jest pewnym uogólnieniem publikacji [6].
5
Content available remote On the asymptotic behavior of solutions to nonlinear differential equations of the second order
Tunç C., Ayhan T.
Commentationes Mathematicae
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2015
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Vol 55, No. 1
1--8
EN
We study the asymptotic behavior of solutions to a nonlinear differential equation of the second order whose coefficient of nonlinearity is a bounded function for arbitrarily large values of x in R. We obtain certain sufficient conditions which guarantee boundedness of solutions, their convergence to zero as x→∞ and their unboundedness
6
Content available About sign-constancy of Green's functions for impulsive second order delay equations
Domoshnitsky A., Landsman G., Yanetz S.
Opuscula Mathematica
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2014
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Vol. 34, no. 2
339--362
EN
We consider the following second order differential equation with delay [formula] In this paper we find necessary and sufficient conditions of positivity of Green's functions for this impulsive equation coupled with one or two-point boundary conditions in the form of theorems about differential inequalities. By choosing the test function in these theorems, we obtain simple sufficient conditions. For example, the inequality [formula] is a basic one, implying negativity of Green's function of two-point problem for this impulsive equation in the case 0<γi≤1, 0<δi≤1 for i=1,…,p.
7
Content available remote On mild solutions of nonlocal second order semilinear functional integro-differential equations
Jain R. S., Dhakne M. B.
Fasciculi Mathematici
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2014
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Nr 53
65--75
EN
In the present paper, we investigate the existence, uniqueness and continuous dependence on initial data of mild solutions of second order nonlocal semilinear functional integro-differential equations of more general type with delay in Banach spaces. Our analysis is based on the theory of strongly continuous cosine family of operators and modified version of Banach contraction theorem.
8
Content available remote MRd - NRd interaction curves with analysis of second order effects for reinforced concrete columns
Rewers I., Seruga T., Kijania M.
Czasopismo Techniczne. Budownictwo
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2013
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R. 110, z. 2-B
93--110
EN
The paper presents regulations for evaluating MRd – NRd interaction curves for reinforced concrete members subjected to axial force and bending moments in one plane, comparing two simplified methods. An example for application of interaction curves in designing columns was presented. The latter part of the paper consists of two simplified methods of designating second order effects according to EC2 – nominal curvature method, nominal stiffness method. The comparison of them was made with MRd – NRd interaction curves.
PL
W artykule przedstawiono zasady wykonywania krzywych interakcji MRd – NRd dla przekrojów elementów żelbetowych, obciążonych siłą osiową i momentem zginającym w jednej płaszczyźnie, porównując dwie metody uproszczone ich opracowywania. Zaprezentowano również przykład zastosowania krzywych interakcji do doboru zbrojenia słupów krępych. W dalszej części pracy zawarto porównanie dwóch uproszczonych metod wyznaczania efektów II rzędu wg EC2 – metody nominalnej krzywizny i metody nominalnej sztywności, wykonane przy pomocy krzywych interakcji MRd – NRd.
9
Content available Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments
Elabbasy E. M., Hassan T. S., Moaaz O.
Opuscula Mathematica
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2012
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Vol. 32, no. 4
719-730
EN
Oscillation criteria are established for second order nonlinear neutral differential equations with deviating arguments of the form [formula] where α > 0 and z(t) = x(t) + p(t)x(t - ϒ). Our results improve and extend some known results in the literature. Some illustrating examples are also provided to show the importance of our results.
10
Content available An abstract nonlocal second order evolution problem
Byszewski L., Winiarska T.
Opuscula Mathematica
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2012
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Vol. 32, no. 1
75-82
EN
The aim of the paper is to prove theorems on the existence and uniqueness of mild and classical solutions of a semilinear evolution second order equation together with nonlocal conditions. The theory of strongly continuous cosine families of linear operators in a Banach space is applied.
11
Content available Oscillation theorems concerning non-linear differential equations of the second order
Elabbasy E.M., Elzeiny Sh.R.
Opuscula Mathematica
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2011
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Vol. 31, no. 3
373-391
EN
This paper concerns the oscillation of solutions of the differential eq. [r,(t) ψ(x(t)) ƒ (x(t))] + q(t) φ (g(x(t)), r(t)ψ(x(t))=0 where uφ(u,v) > 0 for all u ≠ 0, xg(x)>0, xf(x)>0 for all x ≠ 0, ψ(x)>0 for all x ∈ R, r(t)>0 for t≥t0>0 and q is of arbitrary sign. Our results complement the results in [A.G. Kartsatos, On oscillation of nonlinear quations of second order, J. Math. Anal. Appl. 24 (1968), 665-668], and improve a number of existing oscillation criteria. Our main results are illustrated with examples.
12
Content available remote Approximate solutions of a certain second order integrodifferential equation
Pachpatte B. G.
Fasciculi Mathematici
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2010
|
Nr 45
99-109
EN
The main aim of this paper is to study the approximate solutions of a certain second order Volterra type integrodifferential equation with given initial values. A variant of a certain basic integral inequality with explicit estimate is used to establish the results.
13
Content available remote Fundamental solution with weak singularity
Winiarska T.
Bulletin of the Polish Academy of Sciences. Mathematics
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2001
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Vol. 49, no 1
81-90
EN
The main goal of the paper is to present construction the fundamental solution with weak singularity for the evolution equation of second order.
14
Content available remote Resolution of a complete abstract second order differential equation of elliptic type
Labbas R., El Haial A.
Demonstratio Mathematica
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1999
|
Vol. 32, nr 4
745-748
EN
By application of function theoretic methods in partial differential equations (PDE), a nonlinear system of equations, elliptic in the sense of Lavrentiev with a linear boundary condition is investigated. Existence, uniqueness and stability for the boundary value problem (BVP) with degeneration of ellipticity have been proved.
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