Multiplicity and concentration of solutions for fourth-order elliptic equations with mixed nonlinearity

Date

2017-10-10

Authors

Zhang, Wen
Tang, Xianhua
Zhang, Jian
Luo, Zhiming

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

This article concerns the fourth-order elliptic equation ∆2u - ∆u + λV(x)u = ƒ(x, u) + μξ(x)|u|p-2u, x ∈ ℝN, u ∈ H2(ℝN), where λ > 0 is a parameter, V ∈ C(ℝN, ℝ) and V-1(0) has nonempty interior. Under some mild assumptions, we establish the existence of two nontrivial solutions. Moreover, the concentration of these solutions is explored on the set V-1(0) as λ → ∞. As an application, we give the similar results and concentration phenomenona for the above problem with concave and convex nonlinearities.

Description

Keywords

Fourth-order elliptic equations, Concentration, Mixed nonlinearity, Concave-convex nonlinearity, Variational methods

Citation

Zhang, W., Tang, X., Zhang, J., & Luo, Z. (2017). Multiplicity and concentration of solutions for fourth-order elliptic equations with mixed nonlinearity. Electronic Journal of Differential Equations, 2017(250), pp. 1-15.

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Attribution 4.0 International

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