Existence of solutions for Kirchhoff type equations with unbounded potential

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. <i>Electronic Journal of Differential Equations, 2017</i>(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.

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