Existence of nontrivial solutions for Schrodinger-Kirchhoff equations with indefinite potentials
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Date
2023-02-10
Authors
Jiang, Shuai
Yin, Li-Feng
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider a class of Schrödinger-Kirchhoff equations in R3 with a general nonlinearity g and coercive sign-changing potential V so that the Schrödinger operator -aΔ +V is indefinite. The nonlinearity considered here satisfies the Ambrosetti-Rabinowitz type condition g(t)t≥μ G(t)>0 with μ>3. We obtain the existence of nontrivial solutions for this problem via Morse theory.
Description
Keywords
Schrödinger-Kirchhoff equations, Palais-Smale condition, Morse theory
Citation
Jiang, S., & Yin, L. F. (2023). Existence of nontrivial solutions for Schrodinger-Kirchhoff equations with indefinite potentials. <i>Electronic Journal of Differential Equations, 2023</i>(13), pp. 1-15.