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一类p(x)-Laplacian问题弱解的存在性

肖成河、杨姗姗

2011哈尔滨商业大学学报：自然科学版Computer Science被引 0

摘要

Based on the theory of the variable exponent Lebesgue spaces L(superscript p (x)) (Ω) and Sobolev spaces W(superscript k, p (x)) (Ω), this paper studied the following p (x) -Laplacian problem: (The equation is abbreviated) Where Ω⊂R(superscript N) was a bounded domain with smooth boundary and 0＜d＜∞, λ＞0 were constant. Applying the mountain pass lemma, the existence of solution for the above-mentioned p (x) Laplacian problem with principal parts-div [(d+|u|^2) p(x)/2-1▽u] was proved and in the superlinear case.

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