R~N上一类p(x)-Laplacian方程的无穷多解问题

该文主要讨论了如下p(x)-Laplacian算子方程的解.其中1P-≤p(x)≤P+N.得到了上述方程在变指数Sobolev空间W~(1,p(x))(R~N)中的一列能量值趋向正无穷的解.

Multiple Solutions for a Class of p(x)-Laplacian Problems in R~N

In this paper, the authors study the solutions to the following p(x)-Laplacian problem -div(|\nabla_u|^p(x)-2nabla_u)+|u|^p(x)-2u=f ₁(x, u)+f ₂(x, u),       x ∈ R^N.  where 1< p _- ≤ p(x) ≤ p₊ < N.  Based on the theory of the variable exponent Sobolev space W^{1, p(x)} (R^N) it is showed that the above problem possesses a sequence of solutions associated with a sequence of positive energies going toward infinity.