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- W3055295260 abstract "We consider the equation $Delta_x u+u_{yy}+f(u)=0, x=(x_1,dots,x_N)inmathbb{R}^N, yin mathbb{R},$ where $Ngeq 2$ and $f$ is a sufficiently smooth function satisfying $f(0)=0$, $f'(0)<0$, and some natural additional conditions. We prove that the equation possesses uncountably many positive solutions (disregarding translations) which are radially symmetric in $x'=(x_1,dots,x_{N-1})$ and decaying as $|x'|toinfty$, 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." @default.
- W3055295260 created "2020-08-24" @default.
- W3055295260 creator A5009669591 @default.
- W3055295260 creator A5044928606 @default.
- W3055295260 date "2020-08-19" @default.
- W3055295260 modified "2023-10-01" @default.
- W3055295260 title "The existence of partially localized periodic-quasiperiodic solutions and related KAM-type results for elliptic equations on the entire space" @default.
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