Translator Disclaimer
2007 A unified approach for multiple constant sign and nodal solutions
D. Motreanu, V. V. Motreanu, N. S. Papageorgiou
Adv. Differential Equations 12(12): 1363-1392 (2007).

Abstract

We consider a nonlinear elliptic equation driven by the $p$-Laplacian with Dirichlet boundary condition. Using variational techniques, combined with the method of upper-lower solutions and suitable truncation arguments, we establish the existence of at least six nontrivial solutions: two positive, two negative and two nodal (sign-changing) solutions. Our framework of analysis incorporates both coercive and $p-1$-superlinear problems. Also, the result on multiple constant sign solution incorporates the case of concave-convex nonlinearities.

Citation

Download Citation

D. Motreanu. V. V. Motreanu. N. S. Papageorgiou. "A unified approach for multiple constant sign and nodal solutions." Adv. Differential Equations 12 (12) 1363 - 1392, 2007.

Information

Published: 2007
First available in Project Euclid: 18 December 2012

zbMATH: 1167.35372
MathSciNet: MR2382729

Subjects:
Primary: 35J65
Secondary: 35J20, 35J25, 47J30, 49R50

Rights: Copyright © 2007 Khayyam Publishing, Inc.

JOURNAL ARTICLE
30 PAGES


SHARE
Vol.12 • No. 12 • 2007
Back to Top