MULTIPLICITY OF 2-NODAL SOLUTIONS OF THE YAMABE EQUATION

被引：0

作者：

Ortiz, Jorge davila ^{[1
]}

Gonzalez, Hector barrantes ^{[2
]}

Lima, Isidro h. munive ^{[3
]}

机构：

[1] ITESM, Dept Engn & Sci, Campus Leon Guanajuato, Leon Guanajuato 37190, Mexico

[2] Univ Costa Rica, Sede Occidente, Dept Ciencias Nat, Secc Matemat, San Jose 20201, Costa Rica

[3] Univ Guadalajara, Dept Math, CUCEI, Guadalajara 44430, Mexico

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2024年 / 64卷 / 01期

关键词：

Yamabe equation; nodal solution; gradient flow; center of mass; NONLINEAR ELLIPTIC PROBLEM; SCALAR CURVATURE; INVARIANT;

D O I：

10.12775/TMNA.2023.062

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a closed Riemannian manifold ( M,g ), we use the gradient flow method and Sign-Changing Critical Point Theory to prove multiplicity results for 2-nodal solutions of a sub critical non-linear equation on ( M,g ), see (1.1) below. If ( N, h ) is a closed Riemannian manifold of constant positive scalar curvature our result gives multiplicity results for the Yamabe-type equation on the Riemannian product (M x N, g +epsilon h), for epsilon > 0 small.

引用

页码：361 / 379

页数：19

共 50 条

[41] Multiplicity result for a nonhomogeneous Yamabe type equation involving the Kohn Laplacian
Maalaoui, Ali
Martino, Vittorio
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 399 (01) : 333 - 339
[42] Asymptotic Expansions of Solutions of the Yamabe Equation and theσk-Yamabe Equation near Isolated Singular Points
Han, Qing
Li, Xiaoxiao
Li, Yichao
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2021, 74 (09) : 1915 - 1970
[43] 2-nodal domain theorems for higher-dimensional circle bundles
Jung, Junehyuk
Zelditch, Steve
JOURNAL OF SPECTRAL THEORY, 2024, 14 (04) : 1451 - 1474
[44] An Upper Bound for the Least Energy of a Nodal Solution to the Yamabe Equation on the Sphere
Clapp, Monica
Pistoia, Angela
Weth, Tobias
MINIMAX THEORY AND ITS APPLICATIONS, 2022, 7 (02): : 173 - 184
[45] Nodal solutions for the Choquard equation
Ghimenti, Marco
Van Schaftingen, Jean
JOURNAL OF FUNCTIONAL ANALYSIS, 2016, 271 (01) : 107 - 135
[46] Solutions of the Yamabe Equation by Lyapunov-Schmidt Reduction
Davila, Jorge
Munive, Isidro H.
JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (08) : 8080 - 8104
[47] Isolated Singularities of Solutions to the Yamabe Equation in Dimension 6
Xiong, J.
Zhang, L.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2022, 2022 (12) : 9571 - 9597
[48] On the Multiplicity of Nodal Solutions to a Singularly Perturbed Neumann Problem
Anna Maria Micheletti
Angela Pistoia
Mediterranean Journal of Mathematics, 2008, 5 : 285 - 294
[49] On the Multiplicity of Nodal Solutions to a Singularly Perturbed Neumann Problem
Micheletti, Anna Maria
Pistoia, Angela
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2008, 5 (03) : 285 - 294
[50] Multiplicity of positive and nodal solutions for scalar field equations
Cerami, Giovanna
Molle, Riccardo
Passaseo, Donato
JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (10) : 3554 - 3606

← 1 2 3 4 5 →