On Pairs of Positive Solutions for a Class of Semilinear Elliptic Problems.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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In this paper the author discuss the Dirichlet problem -delta u fu 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
- Theoretical Mathematics