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A sign-changing solution for a superlinear Dirichlet problem, II

Citace: [] CASTRO, A., DRÁBEK, P., NEUBERGER, J. A sign-changing solution for a superlinear Dirichlet problem, II. Electronic Journal of Differential Equations, 2003, roč. 0, č. 10, s. 101-107. ISSN: 1072-6691
Druh: ČLÁNEK
Jazyk publikace: eng
Anglický název: A sign-changing solution for a superlinear Dirichlet problem, II
Rok vydání: 2003
Autoři: Alfonso Castro , Pavel Drábek , John M. Neuberger
Abstrakt EN: In previous work by Castro, Cossio and Neuberger [2], it was shown that a superliner Dirichlet problem has at least three nontrivial solutions when the derivative of the nonlinearity at zero is less than the first eigenvalue of $-\Delta$ with zero Dirichlet boundary condition. One of these solutions changes sign exactly-once and the other two are of one sign. In this paper we show that when this derivative is between the k-th and k+1-st eigenvalues there still exists a solution which changes sign at most k times. In particular when k=1 the sign-changing exactly-once soution persists although one-sign solutions no longer exist.
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