A Sign-Changing Solution for a Superlinear Dirichlet Problem
نویسندگان
چکیده
We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once. The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. If nondegenerate, the one sign solutions are of Morse index 1 and the signchanging solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12].
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