【摘要】 研究一个含凹凸非线性的参数型p(x)-7Laplace方程的Dirichlet问题的正解的存在性,在该方程中,超线性项不需要满足Ambrosetti-Rabinowitz条件。利用基于临界点理论的变分方法和Ekeland变分原理,对于取值较小的参数,证明了的所研究的问题至少有两个非平凡的光滑正解。更多还原

【Abstract】 In this paper,a nonlinear parametric Dirichlet problem,driven by the anisotropic p-Laplacian with the combined effects of concave and convex terms,is studied.In this problem,the superlinear nonlinearity needs not satisfy the Ambrosetti-Rabinowitz condition.Using variational methods based on the critical point theory and the Ekeland variational principle,we show that for small values of the parameter,the problem has at least two nontrivial smooth positive solutions.更多还原