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Existence of three solutions for a class of elliptic eigenvalue problems

โœ Scribed by B. Ricceri

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
726 KB
Volume
32
Category
Article
ISSN
0895-7177

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โœฆ Synopsis

In

this paper, we consider a problem of the type -AU = X(j(u)+pg(u))

in R, ~10~ = 0, where R c R" is an open-bounded set, f,g are continuous real functions on Fl, and X,/J E R. As an application of a new approach to nonlinear eigenvalues problems, we prove that, under suitable hypotheses, if 1~1 is small enough, then there is some X > 0 such that the above problem has at least three distinct weak solutions in W,$' (S-Z).

๐Ÿ“œ SIMILAR VOLUMES

Large and Small Solutions of a Class of
Large and Small Solutions of a Class of Quasilinear Elliptic Eigenvalue Problems
โœ Zongming Guo; J.R.L Webb ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 330 KB

Existence and uniqueness results for large positive solutions are obtained for a class of quasilinear elliptic eigenvalue problems in general bounded smooth domains via a generalization of a sweeping principle of Serrin. The nonlinear terms of the problems can be negative in some intervals. The exis