Positive solutions for nonlinear elliptic problems of p-Laplacian type on RN without (AR) condition. (February 2015)

• Record Type: Journal Article
• Authors: Ge, Bin; Zhou, Qingmei; Zu, Li
• Is Part Of: Nonlinear analysis. Volume 21(2015)
• Page Start: 99
• Page End: 109
• Publication Date: 2015-02
• Subjects: p-Laplacian -- Nonhomogeneous -- Cerami sequences -- Mountain Pass Theorem; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2014.07.002
• Languages: English
• ISSNs: 1468-1218

Abstract

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.