R^(N)中含Ф-Laplace算子和凹凸非线性项的拟线性椭圆型方程解的存在性  

Existence of solutions for quasilinear elliptic equation with Φ-Laplacian operator and concave-convex nonlinearities

作　　者：孙爱群 贾高[1] SUN Ai-qun;JIA Gao(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《高校应用数学学报（A辑）》2021年第3期319-330,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然基金(11171220)。

摘　　要：该文研究了全空间中一类含Ф-Laplace算子和凹凸非线性项的拟线性椭圆型方程非平凡解的存在性和多重性.利用Nehari流形方法和纤维映射等技巧,在参数较小的情况下,得到方程至少有两个非平凡解,其中一个是基态解.The paper deals with the existence and multiplicity results of nontrivial solutions to a quasilinear elliptic problem with Φ-Laplacian operator and concave-convex nonlinearities on RN.Nehari manifold and fibering maps are used to obtain the existence of two nontrivial solutions for λ is small enough. Moreover, one of them is a ground state solution.

关 键 词：拟线性椭圆型方程 Nehari流形方法 纤维映射 凹凸非线性项 

分 类 号：O175.25[理学—数学]