Perturbations near resonance for the p-Laplacian in ℝN. (25th June 2002)

• Record Type: Journal Article
• Authors: Ma, To Fu; Pelicer, Maurício Luciano
• Is Part Of: Abstract and applied analysis. Volume 7:Number 6(2002)
• Page Start: 323
• Page End: 334
• Publication Date: 2002-06-25
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/S1085337502203073
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We study a multiplicity result for the perturbedp -Laplacian equation− Δ p u − λ g ( x ) | u | p − 2 u = f ( x, u ) + h ( x ) in ℝ N, where1 < p < N andλ is nearλ 1, the principal eigenvalue of the weighted eigenvalue problem− Δ p u = λ g ( x ) | u | p − 2 u inℝ N . Depending on which sideλ is fromλ 1, we prove the existence of one or three solutions. This kind of result was firstly obtained by Mawhin and Schmitt (1990) for a semilinear two-point boundary value problem.