Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof |
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Authors: | B Breuer M Plum |
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Institution: | a Math. Inst.I, Englerstraße 2, Universität Karlsruhe, D-76128 Karlsruhe, Germany b Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA |
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Abstract: | We prove the first genuine “partial differential equation” result on a conjecture concerning the number of solutions of second-order elliptic boundary value problems with a nonlinearity which grows superlinearly at +∞. The proof makes massive use of computer assistance: After approximate solutions have been computed by a numerical mountain pass algorithm, combined with a Newton iteration to improve accuracy, a fixed point argument is used to show the existence of exact solutions close to the approximations. |
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Keywords: | Semilinear elliptic boundary value problem Multiplicity of solutions Computer-assisted proof |
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