On Pairs of Positive Solutions for a Class of Semilinear Elliptic Problems.

Abstract

In this paper the author discuss the Dirichlet problem -delta u = f(u) in omega, u greater than O in omega, u = O on curly d omega under the hypotheses of sublinearity at O and superlinearity at + infinity. The dominating theme throughout the paper is that of a supersolution of (1). They prove theorems on the existence of two solutions whenever problem (1) possesses a supersolution, using topological degree arguments or variational methods according to the type of growth of f at + infinity. Also treated are questions of existence of supersolutions and their actual construction. Schwarz symmetrization techniques are used to obtain supersolutions from solutions of associated symmetrized problems. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1984
Accession Number
ADA141504

Entities

People

  • D. G. De Figueiredo
  • Pierre Louis Lions

Organizations

  • University of Wisconsin–Madison

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  • C4I

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  • Mathematics

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