Two nontrivial solutions of boundary-value problems for semilinear Δ γ -differential equations

被引：15

作者：

Luyen, D. T. ^{[1
]}

机构：

[1] Hoa Lu Univ, Dept Math, Ninh Nhat Ninh Binh City, Vietnam

来源：

MATHEMATICAL NOTES | 2017年 / 101卷 / 5-6期

关键词：

Semilinear degenerate elliptic equations; critical points; two solutions; multiple solutions; HEISENBERG-GROUP; EXISTENCE;

D O I：

10.1134/S0001434617050078

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 multiple solutions for the boundary-value problem Delta(gamma)u + f(x,u) = 0 in Omega, u = 0 on partial derivative Omega where Omega is a bounded domain with smooth boundary in R-N (N >= 2) and Delta(gamma) is the subelliptic operator of the type Delta gamma u = Sigma xj (gamma j2xju), xju=u/xj; gamma =(gamma 1,gamma 2,...,gamma N). We use the three critical point theorem.

引用

页码：815 / 823

页数：9

共 22 条

[1] MULTIPLE NONTRIVIAL SOLUTIONS OF RESONANT AND NONRESONANT ASYMPTOTICALLY LINEAR-PROBLEMS [J].

AHMAD, S .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 96 (03) :405-409

[2]

Ambrosetti A., 1979, Nonlinear Anal, V3, P635, DOI [10.1016/0362-546X(79)90092-0, DOI 10.1016/0362-546X(79)90092-0]

[3] Liouville-type theorems for elliptic inequalities involving the Δλ-Laplace operator [J].

Cung The Anh ;

Bui Kim My .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2016, 61 (07) :1002-1013

[4] Existence of solutions to Δλ-Laplace equations without the Ambrosetti-Rabinowitz condition [J].

Cung The Anh ;

Bui Kim My .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2016, 61 (01) :137-150

[5] Global attractor of the Cauchy problem for a semilinear degenerate damped hyperbolic equation involving the Grushin operator [J].

Duong Trong Luyen ;

Nguyen Minh Tri .

ANNALES POLONICI MATHEMATICI, 2016, 117 (02) :141-161

[6] EXISTENCE AND NONEXISTENCE RESULTS FOR SEMILINEAR EQUATIONS ON THE HEISENBERG-GROUP [J].

GAROFALO, N ;

LANCONELLI, E .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1992, 41 (01) :71-98

[7]

Grusin V. V., 1970, Mat. Sb. (N.S.), V83, P456

[8] MULTIPLE NONTRIVIAL SOLUTIONS OF SEMILINEAR ELLIPTIC-EQUATIONS [J].

HIRANO, N .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 103 (02) :468-472

[9]

JERISON D, 1987, J DIFFER GEOM, V25, P167

[10] THE DIRICHLET PROBLEM FOR THE KOHN-LAPLACIAN ON THE HEISENBERG-GROUP .2. [J].

JERISON, DS .

JOURNAL OF FUNCTIONAL ANALYSIS, 1981, 43 (02) :224-257

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