STRUCTURE OF NONNEGATIVE NONTRIVIAL AND POSITIVE SOLUTIONS OF SINGULARLY PERTURBED p-LAPLACE EQUATIONS

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (8): 929-936.

STRUCTURE OF NONNEGATIVE NONTRIVIAL AND POSITIVE SOLUTIONS OF SINGULARLY PERTURBED p-LAPLACE EQUATIONS

张正策, 李开泰

College of Sciences, Xi’an Jiaotong University, Xi’an 710049, P. R. China

收稿日期:2002-11-05 修回日期:2004-03-08 出版日期:2004-08-18 发布日期:2004-08-18
基金资助:
the National Key Basic Research Development Project Program of China(1999032801); the National Natural Science Foundation of China(10371095)

STRUCTURE OF NONNEGATIVE NONTRIVIAL AND POSITIVE SOLUTIONS OF SINGULARLY PERTURBED p-LAPLACE EQUATIONS

ZHANG Zheng-ce, LI Kai-tai

College of Sciences, Xi’an Jiaotong University, Xi’an 710049, P. R. China

Received:2002-11-05 Revised:2004-03-08 Online:2004-08-18 Published:2004-08-18
Supported by:
the National Key Basic Research Development Project Program of China(1999032801); the National Natural Science Foundation of China(10371095)

摘要/Abstract

摘要： Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub-and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and positive intermediate spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer were estimated when the parameter is sufficiently small.

关键词: p-Laplace equation, nonnegative nontrivial solution, positive solution, spike-layer solution, sub-and supersolution

Abstract: Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub-and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and positive intermediate spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer were estimated when the parameter is sufficiently small.

Key words: p-Laplace equation, nonnegative nontrivial solution, positive solution, spike-layer solution, sub-and supersolution

中图分类号:

O175.25

张正策;李开泰. STRUCTURE OF NONNEGATIVE NONTRIVIAL AND POSITIVE SOLUTIONS OF SINGULARLY PERTURBED p-LAPLACE EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(8): 929-936.

ZHANG Zheng-ce;LI Kai-tai . STRUCTURE OF NONNEGATIVE NONTRIVIAL AND POSITIVE SOLUTIONS OF SINGULARLY PERTURBED p-LAPLACE EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(8): 929-936.

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STRUCTURE OF NONNEGATIVE NONTRIVIAL AND POSITIVE SOLUTIONS OF SINGULARLY PERTURBED p-LAPLACE EQUATIONS

STRUCTURE OF NONNEGATIVE NONTRIVIAL AND POSITIVE SOLUTIONS OF SINGULARLY PERTURBED p-LAPLACE EQUATIONS

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