The Existence of Partially Localized Periodic-Quasiperiodic Solutions and Related KAM-Type Results for Elliptic Equations on the Entire Space

被引：2

作者：

Polacik, Peter ^{[1
]}

Valdebenito, Dario A. ^{[2
]}

机构：

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[2] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2022年 / 34卷 / 04期

关键词：

Elliptic equations; Entire solutions; Quasiperiodic solutions; Partially localized solutions; Center manifold; KAM theorems; PARTIAL-DIFFERENTIAL-EQUATIONS; POSITIVE SOLUTIONS; STATE SOLUTIONS; CENTER MANIFOLD; WAVE-SOLUTIONS; GROUND-STATES; UNIQUENESS; SYSTEMS; DELTA-U+F(U)=0; DYNAMICS;

D O I：

10.1007/s10884-020-09925-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the equation Delta(x)u + u(yy) + f(u) = 0, x = (x(1), ... , x(N)) is an element of R-N, y is an element of R, (1) where N >= 2 and f is a sufficiently smooth function satisfying f(0) = 0, f'(0) < 0, and some natural additional conditions. We prove that equation (1) possesses uncountably many positive solutions (disregarding translations) which are radially symmetric in x' = (x(1), ... , x(N-1)) and decaying as vertical bar x'vertical bar -> infinity, periodic in x(N), and quasiperiodic in y. Related theorems for more general equations are included in our analysis as well. Our method is based on center manifold and KAM-type results.

引用

页码：3035 / 3056

页数：22

共 10 条

[1] The Existence of Partially Localized Periodic–Quasiperiodic Solutions and Related KAM-Type Results for Elliptic Equations on the Entire Space
Peter Poláčik
Darío A. Valdebenito
[J]. Journal of Dynamics and Differential Equations, 2022, 34 : 3035 - 3056
[2] EXISTENCE OF QUASIPERIODIC SOLUTIONS OF ELLIPTIC EQUATIONS ON THE ENTIRE SPACE WITH A QUADRATIC NONLINEARITY
Polacik, Peter
Valdebenito, Dario A.
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Valdebenito, Dario A.
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