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A Note on Multiple Solutions of Some Semilinear Elliptic Problems

โœ Scribed by E.N. Dancer; Yihong Du

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
228 KB
Volume
211
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

We discuss the existence of multiple solutions of nonlinear elliptic equations by a combination of variational, topological methods and the generalized Conley index theory. We obtain several positive solutions and sign-changing solutions. Our main point is to show the usefulness of the Morse inequalities for Morse decompositions in the generalized Conley index theory. แฎŠ 1997 Academic Press

In this note we show how topological and variational methods and the generalized Conley index can be combined to give better multiplicity results for the semilinear elliptic problem

ัจD

Here D is a bounded domain in R n with regular enough boundary ัจ D; f :

and n* s ฯฑ for n s 1, 2. We make these assumptions throughout this note.

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ลฝ . ลฝ . decays to zero near ฯฑ provided H t t dt -ฯฑ, where t s max p x . Fur-0 < x <st thermore, they show that this condition on p is nearly optimal.