MULTIPLE SOLUTIONS FOR KIRCHHOFF-TYPE PROBLEMS WITH CRITICAL GROWTH IN RN

被引：1

作者：

Liang, Sihua ^{[1
,2
]}

Zhang, Jihui ^{[3
]}

机构：

[1] Changchun Normal Univ, Coll Math, Changchun 130032, Jilin, Peoples R China

[2] Jilin Univ, Key Lab Symbol Computat & Knowledge Engn, Minist Educ, Changchun 130012, Peoples R China

[3] Nanjing Normal Univ, Inst Math, Sch Math Sci, Nanjing 210046, Jiangsu, Peoples R China

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2017年 / 47卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Kirchhoff-type problems; infinitely many solutions; critical growth; concentration-compactness principle; variational methods; LINEAR SCHRODINGER-EQUATIONS; CONCENTRATION-COMPACTNESS PRINCIPLE; POSITIVE SOLUTIONS; SOLITON-SOLUTIONS; ELLIPTIC PROBLEMS; NONTRIVIAL SOLUTIONS; GLOBAL SOLVABILITY; CRITICAL EXPONENT; CRITICAL SOBOLEV; EXISTENCE;

D O I：

10.1216/RMJ-2017-47-2-527

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the existence of infinitely many solutions for a class of Kirchhoff-type problems with critical growth in R-N. By using a change of variables, the quasilinear equations are reduced to a semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem for suitable positive parameters alpha,beta. The proofs are based on variational methods and the concentration-compactness principle.

引用

页码：527 / 551

页数：25

共 51 条

[1]

[Anonymous], 1986, CBME REGIONAL C SERI

[2]

[Anonymous], 1883, Mechanik

[3]

[Anonymous], 1997, Minimax theorems

[4]

[Anonymous], 1964, Topological Methods in the Theory of Nonlinear Integral Equations

[5]

Autuori G., STATIONARY KIR UNPUB

[6] On the existence of stationary solutions for higher-order p-Kirchhoff problems [J].

Autuori, Giuseppina ;

Colasuonno, Francesca ;

Pucci, Patrizia .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2014, 16 (05)

[7] MULTIPLICITY OF SOLUTIONS FOR ELLIPTIC PROBLEMS WITH CRITICAL EXPONENT OR WITH A NONSYMMETRIC TERM [J].

AZORERO, JG ;

ALONSO, IP .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 323 (02) :877-895

[8]

Azorero JPG, 1998, J DIFFER EQUATIONS, V144, P441

[9] POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS [J].

BREZIS, H ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (04) :437-477

[10] A RELATION BETWEEN POINTWISE CONVERGENCE OF FUNCTIONS AND CONVERGENCE OF FUNCTIONALS [J].

BREZIS, H ;

LIEB, E .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (03) :486-490

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