Existence of positive solutions to perturbed nonlinear Dirichlet problems involving critical growth
Date
2017-02-21
Authors
Zhang, Huixing
Zhang, Ran
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider the following perturbed nonlinear elliptic problem with critical growth
-ε2 ∆u + V(x)u = ƒ(x)|u|p-2u + α/α+β K(x)|u|α-2u|v|β, x ∈ ℝN,
-ε2 ∆v + V(x)v = g(x)|v|p-2 v + β/+β K(x)|u|α|v|β-2v, x ∈ ℝN,
u(x), v(x) → 0 as |x| → ∞.
Using variational methods, we prove the existence of positive solutions.
Description
Keywords
Perturbed nonlinear Dirichlet problem, Critical growth, Palais-Smale condition, Variational methods
Citation
Zhang, H., & Zhang, R. (2017). Existence of positive solutions to perturbed nonlinear Dirichlet problems involving critical growth. <i>Electronic Journal of Differential Equations, 2017</i>(54), pp. 1-11.
Rights
Attribution 4.0 International