EXISTENCE OF MULTIPLE SOLUTIONS AND ESTIMATES OF EXTREMAL VALUES FOR A KIRCHHOFF TYPE PROBLEM WITH FAST INCREASING WEIGHT AND CRITICAL NONLINEARITY

被引：0

作者：

Qian, Xiaotao ^{[1
,2
,3
]}

Chen, Jianqing ^{[1
,2
]}

机构：

[1] Fujian Normal Univ, Coll Math & Comp Sci, Qishan Campus, Fuzhou 350108, Fujian, Peoples R China

[2] Fujian Normal Univ, FJKLMAA, Qishan Campus, Fuzhou 350108, Fujian, Peoples R China

[3] Fujian Agr & Forestry Univ, Jinshan Coll, Fuzhou 350002, Fujian, Peoples R China

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年

关键词：

Variational methods; Kirchhoff type equation; critical nonlinearity; multiple solutions; extremal values; SELF-SIMILAR SOLUTIONS; POSITIVE SOLUTIONS; ELLIPTIC-EQUATIONS; CRITICAL EXPONENT;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study the Kirchhoff type problem - (a +epsilon integral K-R3(x)vertical bar del u vertical bar(2)dx) div( K(x)del u) = lambda K(x) f (x) vertical bar u vertical bar(q-2)u + K(x)vertical bar u vertical bar(4)u, where x is an element of R-3, 1 < q < 2, K(x) = exp(vertical bar x vertical bar(alpha)/4) with alpha > 2, epsilon > 0 is small enough, and the parameters a, lambda > 0. Under some assumptions on f(x), we establish the existence of two nonnegative nontrivial solutions and obtain uniform lower estimates for extremal values of the problem via variational methods.

引用

页数：19

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