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

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.