REMARKS ON MINIMIZERS FOR (p, q)-LAPLACE EQUATIONS WITH TWO PARAMETERS

被引：19

作者：

Bobkov, Vladimir ^{[1
,2
]}

Tanaka, Mieko ^{[3
]}

机构：

[1] Univ West Bohemia, Dept Math, Univ 8, Plzen 30614, Czech Republic

[2] Univ West Bohemia, NTIS, Fac Appl Sci, Univ 8, Plzen 30614, Czech Republic

[3] Tokyo Univ Sci, Dept Math, Shinjyuku Ku, Kagurazaka 1-3, Tokyo 1628601, Japan

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2018年 / 17卷 / 03期

关键词：

p-Laplacian; (p; q)-Laplacian; nonlinear eigenvalue problem; global minimizer; ground states; Nehari manifold; fibered functional; improved Poincare inequality; POSITIVE SOLUTIONS; P-LAPLACIAN; NODAL SOLUTIONS; REGULARITY; EXISTENCE; ENERGY; EIGENVALUE; SIGN;

D O I：

10.3934/cpaa.2018059

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study in detail the existence, nonexistence and behavior of global minimizers, ground states and corresponding energy levels of the (p, q)-Laplace equation -Delta(p)u - Delta(q)u = alpha vertical bar u vertical bar(p-2)u + beta vertical bar u vertical bar(q-2)u in a bounded domain Omega subset of R-N under zero Dirichlet boundary condition, where p > q > 1 and alpha,beta is an element of R. A curve on the (alpha,beta)-plane which allocates a set of the existence of ground states and the multiplicity of positive solutions is constructed. Additionally, we show that eigenfunctions of the p- and q-Laplacians under zero Dirichlet boundary condition are linearly independent.

引用

页码：1219 / 1253

页数：35

共 39 条

[1]

Aizicovici S, 2015, T AM MATH SOC, V367, P7343

[2]

Alves MJ., 2015, Illinois J. Math, V59, P545, DOI DOI 10.1215/IJM/1475266397

[3]

ANANE A, 1987, CR ACAD SCI I-MATH, V305, P725

[4] MAX-MIN CHARACTERIZATION OF THE MOUNTAIN PASS ENERGY LEVEL FOR A CLASS OF VARIATIONAL PROBLEMS [J].