Open Access
1998 Multiple solutions for a problem with resonance involving the $p$-Laplacian
C. O. Alves, P. C. Carrião, O. H. Miyagaki
Abstr. Appl. Anal. 3(1-2): 191-201 (1998). DOI: 10.1155/S1085337598000517


In this paper we will investigate the existence of multiple solutions for the problem (P)Δpu+g(x,u)=λ1h(x)|u|p2u,inΩ,uH01,p(Ω) where Δpu=div(|u|p2u) is the p-Laplacian operator, ΩN is a bounded domain with smooth boundary, h and g are bounded functions, N1 and 1<p<. Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least three solutions for (P).


Download Citation

C. O. Alves. P. C. Carrião. O. H. Miyagaki. "Multiple solutions for a problem with resonance involving the $p$-Laplacian." Abstr. Appl. Anal. 3 (1-2) 191 - 201, 1998.


Published: 1998
First available in Project Euclid: 8 April 2003

zbMATH: 0968.35047
MathSciNet: MR1700284
Digital Object Identifier: 10.1155/S1085337598000517

Primary: 35A05 , 35A15 , 35J20

Keywords: Critical Sobolev exponents , Mountain pass theorem , Palais-Smale condition , radial solutions

Rights: Copyright © 1998 Hindawi

Vol.3 • No. 1-2 • 1998
Back to Top