Abstract
In this paper, we consider the existence of solutions for the discrete mixed boundary value problems involvingp,q-Laplacian operator. By using critical points theory, we obtain the existence of at least two positive solutions for the boundary value problem under appropriate assumptions on the nonlinearity.
Highlights
In recent years, with the development of mechanical engineering, control system, computer science, and economics, the existence of solutions of difference equations has attracted wide attention
Applying Ricceri variational principle to obtain the existence of multiple solutions [7,8,9], taking the invariant sets of descending flow to prove the existence of sign-changing solutions [10], making the linking theorem to get the existence and multiplicity of periodic solutions [11], and using critical point theory to obtain the existence of homoclinic solutions [12,13,14,15] and heteroclinic solutions [16]
Main Results e main results of this paper are as follows
Summary
With the development of mechanical engineering, control system, computer science, and economics, the existence of solutions of difference equations has attracted wide attention (see [1,2,3,4,5,6]). It is more common to use critical point theory to study Dirichlet boundary value problems (see [19,20,21,22,23]). In [28], D’Aguı et al established the existence of at least two positive solutions for the following discrete Dirichlet boundary value problem:. D’Aguı et al in [29] proved that there are at least two nonzero weak solutions for the following mixed boundary value problem:. As a discrete analogy of the abovementioned problem, we consider the existence of positive solutions for the following discrete mixed boundary value problem: Discrete Dynamics in Nature and Society.
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