TY - JOUR

T1 - Multiplicity of positive solutions for a p-q-laplacian type equation with critical nonlinearities

AU - Hsu, Tsing San

AU - Lin, Huei Li

PY - 2014

Y1 - 2014

N2 - We study the effect of the coefficient f (x) of the critical nonlinearity on the number of positive solutions for a p - q -Laplacian equation. Under suitable assumptions for f (x) and g (x), we should prove that for sufficiently small > 0, there exist at least k positive solutions of the following p - q -Laplacian equation, - p u - q u = f x u | p - 2 u + g x u | r - 2 u in Ω, u = 0 on ∂ Ω, where Ω ⊂ R N is a bounded smooth domain, N > p, 1 < q < N (p - 1) / (N - 1) < p ≤ max { p, p- q / (p - 1) } < r < p ,p = N p / (N - p) is the critical Sobolev exponent, and s u = d i v (| u | s - 2 u is the s -Laplacian of u.

AB - We study the effect of the coefficient f (x) of the critical nonlinearity on the number of positive solutions for a p - q -Laplacian equation. Under suitable assumptions for f (x) and g (x), we should prove that for sufficiently small > 0, there exist at least k positive solutions of the following p - q -Laplacian equation, - p u - q u = f x u | p - 2 u + g x u | r - 2 u in Ω, u = 0 on ∂ Ω, where Ω ⊂ R N is a bounded smooth domain, N > p, 1 < q < N (p - 1) / (N - 1) < p ≤ max { p, p- q / (p - 1) } < r < p ,p = N p / (N - p) is the critical Sobolev exponent, and s u = d i v (| u | s - 2 u is the s -Laplacian of u.

UR - http://www.scopus.com/inward/record.url?scp=84899440149&partnerID=8YFLogxK

U2 - 10.1155/2014/829069

DO - 10.1155/2014/829069

M3 - 文章

AN - SCOPUS:84899440149

SN - 1085-3375

VL - 2014

JO - Abstract and Applied Analysis

JF - Abstract and Applied Analysis

M1 - 829069

ER -