Positive solutions for nonlinear elliptic problems of p-Laplacian type on RN without (AR) condition. (February 2015) - Ge, Bin
Abstract: In this paper, we study the following problem (P) { − Δ p u + | u | p − 2 u = α ( x ) f ( u ), x ∈ R N, u ∈ W 1, p ( R N ), u ( x ) > 0 in R N, where 1 < p ≤ N and α is a positive bounded function. For the case when f ( t ) is asymptotically linear at infinity, the Ambrosetti–Rabinowitz type condition and the monotonicity of f ( t ) t are not assumed; for the case of superlinear at infinity, the Ambrosetti–Rabinowitz type condition is not assumed. Under appropriate assumptions on α and f, we prove that problem(P) has at least one positive solution.