Multiplicity of positive solutions for a class of problems with critical growth in N

Abstract

Using variational methods, we establish the existence and multiplicity of positive solutions for the following class of problems:-Δu + (λV (x) + Z(x))u = βuq + u2*-1, u≥0 in RN, where λ β* (0,∞), q ε (1, 2* - 1), 2* = 2N/(N - 2), N > 3, V,Z : R? RN are continuous functions verifying some hypotheses. © Edinburgh Mathematical Society 2009.