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. <i>Electronic Journal of Differential Equations, 2017</i>(250), pp. 1-15.