本文主要利用拓扑度理论中的不动点定理和变分方法中的极小作用原理及其环绕形式的临界点定理在适当的条件下讨论了一类二阶椭圆边值问题的可解性。
The aim of this thesis is to study the existence of weak solutions for semilinear second order elliptic boundary value problems under suitable conditions through topological and variational methods.
通过极小化作用原理和极小极大方法得到了一类四阶非线性椭圆方程解的存在性和多重性。
The existence and multiplicity results are obtained for a class of fourth-order nonlinear elliptic equations by the least action principle and the minimax methods, respectively.
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