A Multiplicity Result for a Semilinear Dirichlet Problem.
Abstract
In this paper the author considers the number of solutions of the Dirichlet problem for semilinear elliptic equations. Specifically he studies the question of finding solutions u of an equation such as delta u + g(u) = lambda in a bounded domain omega included in R sub n subject to the condition that u vanishes on the boundary of omega. This problem has been intensively studied in the last few years; it arises in many situations such as nonlinear diffusion generated by nonlinear sources, the thermal ignition of gases, and others. This paper derives precise estimates of the number of solutions under assumptions which are natural for these problems thereby complementing results obtained by a number of authors.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1983
- Accession Number
- ADA130492
Entities
People
- J. V. A. Goncalves
Organizations
- University of Wisconsin–Madison