Related papers: On the well posed solutions for nonlinear second o…
Using min-max inequality we investigate the existence of solutions and thier dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle…
We describe the asymptotic behaviour and the stability properties of the solutions to a second order rational difference equation.
The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.
In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii's fixed point theorem on cones, sufficient conditions for the…
By means of classical fixed point index, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of Hammerstein integral equations where the nonlinearities are allowed to…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
This paper extends the discriminant associated to second order linear constant coefficient differential equations to general second order linear differential equations. The main result of this paper is that the discriminant of a second…
We prove the well-posedness results, i.e. existence, uniqueness, and stability, of the solutions to a class of nonlocal fully nonlinear parabolic partial differential equations (PDEs), where there is an external time parameter $t$ on top of…
We study the behaviour of solutions of ordinary differential equations of the second order with singular points, where the coefficients of the second-order derivative vanishes. In particular, we consider solutions entering a singular point…
Selection of 25 examples from extensive nontrivial families for different types of nonlinear PDEs and their formal general solutions are given. The main goal here is to show on examples the types of solvable PDEs and what their general…
We describe some monotone properties of solutions to second order linear difference equations with real constant coefficients. As an application, we give a characterization of the Fibonacci numbers.
We consider existence of periodic boundary value problems of nonlinear second order ordinary differential equations. Under certain half Lipschitzian type conditions several existence results are obtained. As applications positive periodic…
In this article we study solutions to second order linear difference equations with variable coefficients. Under mild conditions we provide closed form solutions using finite continued fraction representations. The proof of the results are…
By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…
The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a…
The main objective of this paper is to study the existence of solutions to some basic fractional difference equations. The tools employed are Krasnosel'skii fixed point theorem which guarantee at least two positive solutions.
This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.
In this paper by exploiting critical point theory, the existence of two distinct nontrivial solutions for a nonlinear algebraic system with a parameter is established. Our goal is achieved by requiring an appropriate behavior of the…
We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley. For the latter two equations these solutions…
In this paper, we study the existence of solutions for second-order non-instantaneous impulsive differential equations with a perturbation term. By variational approach, we obtain the problem has at least one solution under assumptions that…