A Multiplicity Result for a Semilinear Dirichlet Problem

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 tha...

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Bibliographic Details
Main Author: Goncalves,J V A
Format: Report
Language:English
Subjects:
Dirichlet integral
Eigenvalues
Elliptic equations
Equations
Estimates
Nonlinear analysis
Numerical Mathematics
Operators(Mathematics)
Problem solving
Solutions(General)
Variational methods
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Summary: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.