Existence of positive solutions to perturbed nonlinear Dirichlet problems involving critical growth
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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.
CitationZhang, H., & Zhang, R. (2017). Existence of positive solutions to perturbed nonlinear Dirichlet problems involving critical growth. Electronic Journal of Differential Equations, 2017(54), pp. 1-11.
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