Related papers: Existence results and numerical solution of fully …
As is known, the problems for the differential equations with continuously changing order of the derivatives are not considered completely. In this paper we consider the initial and boundary value problems for this type of linear ordinary…
This paper deals with the existence of solutions to a class of fourth order nonlinear elliptic equations. The technique used relies on critical points theory. The solutions appeared as critical points of a functional restricted to a…
We prove existence of positive solutions to a nonlinear fractional boundary value problem. Then, under some mild assumptions on the nonlinear term, we obtain a smart generalization of Lyapunov's inequality. The new results are illustrated…
In this work we provide conditions for the existence of solutions to nonlinear boundary value problems of the form \begin{equation*} y(t+n)+a_{n-1}(t)y(t+n-1)+\cdots a_0(t)y(t)=g(t,y(t+m-1)) \end{equation*} subject to \begin{equation*}…
We study the existence and multiplicity of positive solutions for a nonlinear fourth-order two-point boundary value problem. The approach is based on critical point theorems in conical shells, Krasnoselskii's compression-expansion theorem,…
In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…
This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…
In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…
In this paper we prove the existence of multiple solutions for a quasilinear elliptic boundary value problem, when the p-derivative at zero and the p-derivative at infinity of the nonlinearity are greater than the first eigenvalue of the…
The boundary value problems for linear and nonlinear singular degenerate differential-operator equations are studied. We prove a well-posedeness of linear problem and optimal regularity result for the nonlinear problem which occur in fluid…
We study a Dirichlet-type boundary value problem for a pseudo-differential equation driven by the fractional Laplacian, with a non-linear reaction term which is resonant at infinity between two non-principal eigenvalues: for such equation…
To extract the approximate solutions in the case of nonlinear fractional order differential equations with the homogeneous and nonhomogeneous boundary conditions, the weighted residual method is embedded here. We exploit three methods such…
We consider a nonlinear boundary value problem driven by a nonhomogeneous differential operator. The problem exhibits competing nonlinearities with a superlinear (convex) contribution coming from the reaction term and a sublinear (concave)…
In this article we introduce a simple straightforward and powerful method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of partial differential boundary value problems. The method is…
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones…
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
In this paper, we study the existence, regularity, and approximation of the solution for a class of nonlinear fractional differential equations. {In order to do this}, suitable variational formulations are defined for a nonlinear boundary…
In this paper, we study the existence and multiplicity of positive solutions for a nonlinear fourth-order with multi-point boundary conditions involving an integral boundary condition. The main tool is Krasnosel'skii fixed point theorem on…