Existence of solutions to a generalized quasilinear Schrödinger equation with concave-convex nonlinearities and potentials vanishing at infinity-Reference-Cited by-同舟云学术

Existence of solutions to a generalized quasilinear Schrödinger equation with concave-convex nonlinearities and potentials vanishing at infinity

Published:2023 Issue:11 Volume:8 Page:27684-27711
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Guo Xiaojie,Han Zhiqing

Abstract

<abstract><p>In this paper, we investigate the existence of solutions to a generalized quasilinear Schrödinger equation with concave-convex nonlinearities and potentials vanishing at infinity. Using the mountain pass theorem, we get the existence of a positive solution.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference36 articles.

1. J. F. L. Aires, M. A. S. Souto, Existence of solutions for a quasilinear Schrödinger equation with vanishing potentials, J. Math. Anal. Appl., 416 (2014), 924–946. http://doi.org/10.1016/j.jmaa.2014.03.018

2. C. O. Alves, M. A. S. Souto, Existence of solutions for a class of nonlinear Schrödinger equations with potential vanishing at infinity, J. Differ. Equations, 254 (2013), 1977–1991. http://doi.org/10.1016/j.jde.2012.11.013

3. A. Ambrosetti, V. Felli, A. Malchiodi, Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity, J. Eur. Math. Soc., 7 (2005), 117–144. http://doi.org/10.4171/JEMS/24

4. A. Ambrosetti, P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349–381. https://doi.org/10.1016/0022-1236(73)90051-7

5. A. De Bouard, N. Hayashi, J. C. Saut, Global existence of small solutions to a relativistic nonlinear Schrödinger equation, Commun. Math. Phys., 189 (1997), 73–105. https://doi.org/10.1007/s002200050191