Abstract and Applied Analysis

Multiple Positive Solutions for Semilinear Elliptic Equations in N Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions

Tsing-San Hsu and Huei-Li Lin

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Abstract

We study the existence and multiplicity of positive solutions for the following semilinear elliptic equation - Δ u + u = λ a ( x ) | u | q - 2 u + b ( x ) | u | p - 2 u in N , u H 1 ( 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 .

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 658397, 21 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620739

Digital Object Identifier
doi:10.1155/2010/658397

Mathematical Reviews number (MathSciNet)
MR2669082

Zentralblatt MATH identifier
05791633

Citation

Hsu, Tsing-San; Lin, Huei-Li. Multiple Positive Solutions for Semilinear Elliptic Equations in Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions. Abstr. Appl. Anal. 2010 (2010), Article ID 658397, 21 pages. doi:10.1155/2010/658397. https://projecteuclid.org/euclid.aaa/1288620739


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