Zhang, HuixingZhang, Ran2022-03-302022-03-302017-02-21Zhang, 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. 1-11.1072-6691https://hdl.handle.net/10877/15580We 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.Text11 pages1 file (.pdf)enAttribution 4.0 InternationalPerturbed nonlinear Dirichlet problemCritical growthPalais-Smale conditionVariational methodsArticle