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A Priori Bounds and Multiple Solutions for Superlinear Indefinite Elliptic Problems

✍ Scribed by H. Amann; J. López-Gómez

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
528 KB
Volume
146
Category
Article
ISSN
0022-0396

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✦ Synopsis

In this work we study existence and multiplicity questions for positive solutions of second-order semilinear elliptic boundary value problems, where the nonlinearity is multiplied by a weight function which is allowed to change sign and vanish on sets of positive measure. We do not impose a variational structure, thus techniques from the calculus of variations are not applicable. Under various qualitative assumptions on the nonlinearity we establish a priori bounds and employ bifurcation and fixed point index theory to prove existence and multiplicity results for positive solutions. In an appendix we derive interior L p -estimates for general elliptic systems of arbitrary order under minimal smoothness hypotheses. Special instances of these results are used in the derivation of a priori bounds.

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