On the existence of multiple solutions to boundary value problems for semilinear elliptic degenerate operators

被引:18
作者
Duong Trong Luyen [1 ]
Nguyen Minh Tri [2 ]
机构
[1] Hoa Lu Univ, Dept Math, Ninh Binh, Vietnam
[2] Vietnam Acad Sci & Technol, Inst Math, Hanoi, Vietnam
关键词
Semilinear degenerate elliptic equations; boundary value problems; critical points; perturbation methods; multiple solutions; Grushin operator; CRITICAL-POINT THEORY; TIME BEHAVIOR; EQUATIONS;
D O I
10.1080/17476933.2018.1498086
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 where omega is a bounded domain with smooth boundary in are Caratheodory functions and is the Grushin operator. This result is a generalization of that of Rabinowitz and of Luyen and Tri.
引用
收藏
页码:1050 / 1066
页数:17
相关论文
共 33 条
[1]  
Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7
[2]   MORSE INDEX OF SOME MIN MAX CRITICAL-POINTS .1. APPLICATION TO MULTIPLICITY RESULTS [J].
BAHRI, A ;
LIONS, PL .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1988, 41 (08) :1027-1037
[3]   A PERTURBATION METHOD IN CRITICAL-POINT THEORY AND APPLICATIONS [J].
BAHRI, A ;
BERESTYCKI, H .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1981, 267 (01) :1-32
[4]   Critical point theory on partially ordered Hilbert spaces [J].
Bartsch, T .
JOURNAL OF FUNCTIONAL ANALYSIS, 2001, 186 (01) :117-152
[5]   The multiplicity of solutions in non-homogeneous boundary value problems [J].
Bolle, P ;
Ghoussoub, N ;
Tehrani, H .
MANUSCRIPTA MATHEMATICA, 2000, 101 (03) :325-350
[6]   Lower bounds of eigenvalues for a class of bi-subelliptic operators [J].
Chen, Hua ;
Zhou, Yifu .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 262 (12) :5860-5879
[7]   Lower bounds of Dirichlet eigenvalues for some degenerate elliptic operators [J].
Chen, Hua ;
Luo, Peng .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 54 (03) :2831-2852
[8]   VARIANT OF LUSTERNIK-SCHNIRELMAN THEORY [J].
CLARK, DC .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1972, 22 (01) :65-&
[9]   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
[10]   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