一类四阶边值问题的反对称变号解
Anti-symmetric Sign-changing Solutions of a Class of Fourth-orderBoundary Value Problems
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摘要: 利用Krasnosel`skii不动点定理及解的延拓技巧,证明了一类非线性四阶边值问题,当其非线性项满足某些假设条件时,存在反对称变号解,并对此进一步推广得到了四阶边值问题具有无穷多个反对称变号解的条件.Abstract: The existence of anti-symmetric sign-changing solution for a nonlinear fourth-order boundary value problem is proved by use of Krasnosel`skii fixed point theorem and the continuation techniques of the solution when the non-linear terms meet certain assumed conditions. And through further generalization, the conditions, under which such fourth-order boundary value problems have multiple anti-symmetric sign-changing solutions, were worked out.