Infinitely many homoclinic solutions for sublinear and nonperiodic Schrödinger lattice systems

Partial difference equations have received more and more attention in recent years due to their extensive applications in diverse areas. In this paper, we consider a Dirichlet boundary value problem of the partial difference equation involving the mean curvature operator. By applying critical point theory, the existence of at least three solutions is obtained. Furthermore, under some appropriate assumptions on the nonlinearity, we respectively show that this problem admits at least two or three positive solutions by means of a strong maximum principle. Finally, we present two concrete examples and combine with images to illustrate our main results.

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Infinitely many homoclinic solutions for sublinear and nonperiodic Schrödinger lattice systems

Abstract: By using variational methods we obtain infinitely many nontrivial solutions for a class of nonperiodic Schrödinger lattice systems, where the nonlinearities are sublinear at both zero and infinity.

Cited by 2 publications

References 24 publications

Existence of Infinitely Many Homoclinic Solutions of Discrete Schrödinger Equations With Local Sublinear Terms

Existence of Infinitely Many Homoclinic Solutions of Discrete Schrödinger Equations With Local Sublinear Terms

Three Solutions for a Partial Discrete Dirichlet Problem Involving the Mean Curvature Operator

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