A Dirichlet Problem with In nite Multiplicity
نویسنده
چکیده
We construct examples of strictly convex functions f on (?1; 1) satisfying f 0 (?1) < n 2 < f 0 (1) such that the Dirichlet problem u 00 + f(u) = h(x) in 0; ], u(0) = u() = 0, has an innnite number of solutions, for any choice of h(x). Kaper and Kwong earlier have presented examples with ve solutions to settle a conjecture raised by Lazer and McKenna. Here, we also give a suucient condition for the number of solutions to be nite. Bounds for the number of solutions of a Dirichlet problem are of interest in the study of boundary value problems of semilinear elliptic equations.
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