THE EXISTENCE OF THREE SOLUTIONS FOR p-LAPLACIAN PROBLEMS WITH CRITICAL AND SUPERCRITICAL GROWTH

被引：10

作者：

Zhao, Lin ^{[1
,2
]}

Zhao, Peihao ^{[1
]}

机构：

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

[2] China Univ Mining & Technol, China & Sch Sci, Xuzhou 221116, Peoples R China

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2014年 / 44卷 / 04期

关键词：

Critical point theory; variational methods; three solutions; Moser iteration; CRITICAL SOBOLEV EXPONENTS; LINEAR ELLIPTIC-EQUATIONS; CRITICAL-POINTS THEOREM; POSITIVE SOLUTIONS; VARIATIONAL-METHODS; MULTIPLICITY;

D O I：

10.1216/RMJ-2014-44-4-1383

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we deal with the existence and multiplicity of solutions for the p-Laplacian problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation combining with the Moser iteration, we extend the result obtained by Ricceri [14] to the critical and supercritical case.

引用

页码：1383 / 1397

页数：15

共 20 条

[1] COMBINED EFFECTS OF CONCAVE AND CONVEX NONLINEARITIES IN SOME ELLIPTIC PROBLEMS [J].

AMBROSETTI, A ;

BREZIS, H ;

CERAMI, G .

JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 122 (02) :519-543

[2]

[Anonymous], 1997, Adv. Differ. Equ.

[3] 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

[4] Sobolev versus Holder local minimizers and global multiplicity for some quasilinear elliptic equations [J].

Azorero, JPG ;

Alonso, IP ;

Manfredi, JJ .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2000, 2 (03) :385-404

[5] 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

[6] On an elliptic equation of p-Kirchhoff type via variational methods [J].

Correa, Francisco Julio S. A. ;

Figueiredo, Giovany M. .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2006, 74 (02) :263-277

[7] Positive solutions for some quasilinear equations with critical and supercritical growth [J].

Figueiredo, Giovany M. ;

Furtado, Marcelo F. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 66 (07) :1600-1616

[8] Compact Sobolev embedding theorems involving symmetry and its application [J].

Gao, Juanjuan ;

Zhao, Peihao ;

Zhang, Yong .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2010, 17 (02) :161-180

[9] QUASILINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS [J].

GUEDDA, M ;

VERON, L .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1989, 13 (08) :879-902

[10]

Lions P-L., 1985, Rev. Mat. Iberoamericana, V1, P145, DOI [DOI 10.4171/RMI/6, 10.4171/rmi/6]

← 1 2 →