R^n上p(x)-Laplace型椭圆问题的无穷多解

Infinitely Many Solutions to p(x)-Laplace Type Elliptic Problems in R^n

讨论了涉及一般散度型椭圆算子(p(x)-Laplace算子为其特例)非线性偏微分方程的弱解存在性和多解性问题,假定非线性项f_1,f_2其中之一是超线性的,且满足Ambrosetti-Rabinowitz条件,另一项是次线性的.所采用的方法依赖于变指数Sobolev空间W^(1,p(x))(R^n)理论.主要结果的证明基于喷泉定理和对偶喷泉定理.

In this paper, the existence and multiplicity of weak solutions to nonlinear partial differential equations involving a general elliptic operator in divergence form （in particular, a p（x）-Laplace operator） in Rn are investigated, assumed that one of the nonlinear terms fl and f2 is superlinear and satisfies the Ambrosetti-Rabinowitz type condition and another one is sublinear. Our approach relies on the theory of variable exponent Sobolev space W1,p（x） （Rn）. The proofs of our main results are based on the Fountain theorem and the Dual Fountain theorem.