Semiclassical solutions of perturbed p-Laplacian equations with critical nonlinearity

被引：17

作者：

Lin, Xiaoyan ^{[1
]}

Tang, X. H. ^{[2
]}

机构：

[1] Huaihua Coll, Dept Math, Huaihua 418008, Hunan, Peoples R China

[2] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 413卷 / 01期

关键词：

Perturbed p-Laplacian equation; Semiclassical solution; Sobolev critical exponent; LINEAR SCHRODINGER-EQUATION; BOUND-STATES; EXISTENCE; MULTIPLICITY;

D O I：

10.1016/j.jmaa.2013.11.063

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the perturbed p-Laplacian equation -epsilon(p)Delta(p)u + V(x) vertical bar u vertical bar(p-2)u = K(x) vertical bar u vertical bar(p)*(-2)u + f (x, u), u is an element of W-1,W-p (R-N), where Delta(p)u := div(vertical bar del u vertical bar(p-2)del u) is the p-Laplacian operator with 1 < p < N, p* = pN/(N - p) denotes the Sobolev critical exponent, K(x) is a bounded positive function. Under some mild conditions on V and f we show that the equation has at least one nontrivial solution provided that epsilon < epsilon(0), where the bound so is formulated in terms of p, N, V, K and f. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：438 / 449

页数：12

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