论文标题
涉及可变指数的非线性椭圆方程的弱溶解度
Weak solvability of nonlinear elliptic equations involving variable exponents
论文作者
论文摘要
我们关注的是对DIRICHLET边界价值问题的存在和多样性的研究，涉及$（p（m），\，Q（m）） - $方程和非线性是超级线性的，但不能满足Ambrosetti-Rabinowitz在Sobolev Space的框架中具有完整量化代价的框架中的Ambrosetti-Rabinowitz条件。使用山地定理和喷泉定理证明了主要结果。此外，还提供了一个$（p（m），\，q（m））$方程的示例，该方程还强调了我们理论结果的适用性。
We are concerned with the study of the existence and multiplicity of solutions for Dirichlet boundary value problems, involving the $( p( m ), \, q( m ) )-$ equation and the nonlinearity is superlinear but does not fulfil the Ambrosetti-Rabinowitz condition in the framework of Sobolev spaces with variable exponents in a complete manifold. The main results are proved using the mountain pass theorem and Fountain theorem with Cerami sequences. Moreover, an example of a $( p( m ), \, q( m ) )$ equation that highlights the applicability of our theoretical results is also provided.
