Positive solutions for Kirchhoff-Schrodinger equations via Pohozaev manifold
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Date
2022-11-17
Authors
Hu, Xian
Lan, Yong-Yi
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we consider the Kirchhoff-Schrödinger equation
-((ɑ + b ∫ℝ3 |∇u|2dx) ∆u + λu = k(x)ƒ(u), x ∈ ℝ3,
where u H1(ℝ3), λ > 0, ɑ > 0, b ≥ 0 are real constants, k : ℝ3 → ℝ and ƒ ∈ C (ℝ, ℝ). To overcome the difficulties that k is non-symmetric and the non-linear, and that f is non-homogeneous, we prove the existence a positive solution using projections on a general Pohozaev type manifold, and the linking theorem.
Description
Keywords
Kirchhoff-Schrödinger equation, Pohozaev manifold, Cerami sequence, Linking theorem
Citation
Hu, X., & Lan, Y. Y. (2022). Positive solutions for Kirchhoff-Schrodinger equations via Pohozaev manifold. <i>Electronic Journal of Differential Equations, 2022</i>(75), pp. 1-13.
Rights
Attribution 4.0 International