Existence of solutions for Kirchhoff type equations with unbounded potential
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Date
2017-07-19
Authors
Duan, Yueliang
Zhou, Yinggao
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the Kirchhoff type equation
(α + λ ∫ℝ3 |∇u|2 + λb ∫ℝ3u2) [-∆u + bu] = K(x)|u|p-1u, in ℝ3,
where α, b > 0, p ∈ (2, 5), λ ≥ 0 is a parameter, and K may be an unbounded potential function. By using variational methods, we prove the existence of nontrivial solutions for the above equation. A cut-off functional and some estimates are used to obtain the bounded Palais-Smale sequences.
Description
Keywords
Cut-off functional, Kirchhoff type problem, Unbounded potential, Variational method
Citation
Duan, Y., & Zhou, Y. (2017). Existence of solutions for Kirchhoff type equations with unbounded potential. Electronic Journal of Differential Equations, 2017(184), pp. 1-12.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.