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Quasilinearity below the 1st eigenvalue


Author: Victor L. Shapiro
Journal: Proc. Amer. Math. Soc. 129 (2001), 1955-1962
MSC (2000): Primary 35J60; Secondary 35J35
Published electronically: February 15, 2001
MathSciNet review: 1825902
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Abstract | References | Similar Articles | Additional Information

Abstract:

This paper establishes the existence of two nontrivial weak solutions for a quasilinear Dirichlet problem below the first eigenvalue via the mountain pass theorem.


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Additional Information

Victor L. Shapiro
Affiliation: Department of Mathematics, University of California, Riverside, California 92521-0135
Email: shapiro@math.ucr.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06124-X
Keywords: Quasilinear variational, first eigenvalue, mountain pass theorem, near $p$-homogeneous.
Received by editor(s): September 7, 1999
Published electronically: February 15, 2001
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2001 American Mathematical Society