Multiple positive solutions for semilinear elliptic equations in N involving concave-convex nonlinearities and sign-changing weight functions

Tsing San Hsu; Huei Li Lin

doi:10.1155/2010/658397

Multiple positive solutions for semilinear elliptic equations in N involving concave-convex nonlinearities and sign-changing weight functions

Tsing San Hsu^*, Huei Li Lin

^*Corresponding author for this work

Division of Natural Science

Research output: Contribution to journal › Journal Article › peer-review

6 Scopus citations

Abstract

We study the existence and multiplicity of positive solutions for the following semilinear elliptic equation - δu + u = λa (x) | u | ^{q - 2} u + b (x) | u | ^{p - 2} u in ℝ^N, u ∈ H¹ (ℝ^N), where λ < 0, 1 > q > 2 > p > 2* (2* = 2 N / (N - 2) if N ≥ 3, 2* = ∞ if N = 1,2), a (x), b (x) satisfy suitable conditions, and a (x) may change sign in N.

Original language	English
Article number	658397
Journal	Abstract and Applied Analysis
Volume	2010
DOIs	https://doi.org/10.1155/2010/658397
State	Published - 2010

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title = "Multiple positive solutions for semilinear elliptic equations in N involving concave-convex nonlinearities and sign-changing weight functions",

abstract = "We study the existence and multiplicity of positive solutions for the following semilinear elliptic equation - δu + u = λa (x) | u | q - 2 u + b (x) | u | p - 2 u in ℝN, u ∈ H1 (ℝN), where λ < 0, 1 > q > 2 > p > 2* (2* = 2 N / (N - 2) if N ≥ 3, 2* = ∞ if N = 1,2), a (x), b (x) satisfy suitable conditions, and a (x) may change sign in N.",

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journal = "Abstract and Applied Analysis",

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AU - Hsu, Tsing San

AU - Lin, Huei Li

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N2 - We study the existence and multiplicity of positive solutions for the following semilinear elliptic equation - δu + u = λa (x) | u | q - 2 u + b (x) | u | p - 2 u in ℝN, u ∈ H1 (ℝN), where λ < 0, 1 > q > 2 > p > 2* (2* = 2 N / (N - 2) if N ≥ 3, 2* = ∞ if N = 1,2), a (x), b (x) satisfy suitable conditions, and a (x) may change sign in N.

AB - We study the existence and multiplicity of positive solutions for the following semilinear elliptic equation - δu + u = λa (x) | u | q - 2 u + b (x) | u | p - 2 u in ℝN, u ∈ H1 (ℝN), where λ < 0, 1 > q > 2 > p > 2* (2* = 2 N / (N - 2) if N ≥ 3, 2* = ∞ if N = 1,2), a (x), b (x) satisfy suitable conditions, and a (x) may change sign in N.

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DO - 10.1155/2010/658397

M3 - 文章

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VL - 2010

JO - Abstract and Applied Analysis

JF - Abstract and Applied Analysis

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ER -

Multiple positive solutions for semilinear elliptic equations in N involving concave-convex nonlinearities and sign-changing weight functions

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