Zobrazeno 1 - 10
of 242
pro vyhledávání: '"35B08"'
Autor:
Geng, Zhiyuan
For the two dimensional Allen-Cahn system with a triple-well potential, previous results established the existence of a minimizing solution $u:\mathbb{R}^2\rightarrow\mathbb{R}^2$ with a triple junction structure at infinity. We show that along each
Externí odkaz:
http://arxiv.org/abs/2412.02954
We study degenerate quasilinear elliptic equations on Riemannian manifolds and obtain several Liouville theorems. Notably, we provide rigorous proof asserting the nonexistence of positive solutions to the subcritical Lane-Emden-Fowler equations over
Externí odkaz:
http://arxiv.org/abs/2411.06956
We study the fractional Schr\"odinger equations with a vanishing parameter: $$ (-\Delta)^s u+u =|u|^{p-2}u+\lambda|u|^{q-2}u \text{ in }\mathbb{R}^N,\quad u \in H^s(\mathbb{R}^N),$$ where $s\in(0,1)$, $N>2s$, $2
Externí odkaz:
http://arxiv.org/abs/2410.03233
In this paper we consider a competitive weakly coupled elliptic system in which each species is attracted to a small region and repelled from its complement. In this setting, we establish the existence of infinitely many solutions and of a nonnegativ
Externí odkaz:
http://arxiv.org/abs/2407.20125
We are interested in finding prescribed $L^2$-norm solutions to inhomogeneous nonlinear Schr\"{o}dinger (INLS) equations. For $N\ge 3$ we treat the equation with combined Hardy-Sobolev power-type nonlinearities $$ -\Delta u+\lambda u=\mu|x|^{-b}|u|^{
Externí odkaz:
http://arxiv.org/abs/2407.09737
Autor:
De Regibus, Fabio, Ruiz, David
In this paper we show the existence of strictly monotone heteroclinic type solutions of semilinear elliptic equations in cylinders. The motivation of this construction is twofold: first, it implies the existence of an entire bounded solution of a sem
Externí odkaz:
http://arxiv.org/abs/2407.04546
Autor:
Ogden, W. Jacob, Yuan, Yu
Constant rank theorems are obtained for saddle solutions to the special Lagrangian equation and the quadratic Hessian equation. The argument also leads to Liouville type results for the special Lagrangian equation with subcritical phase, matching the
Externí odkaz:
http://arxiv.org/abs/2405.18603
Autor:
Kon'kov, A. A., Shishkov, A. E.
We study systems of the differential inequalities $$ \left\{ \begin{aligned} & - \operatorname{div} A_1 (x, \nabla u_1) \ge F_1 (x, u_2) & \mbox{in } {\mathbb R}^n, & - \operatorname{div} A_2 (x, \nabla u_2) \ge F_2 (x, u_1) & \mbox{in } {\mathbb R}^
Externí odkaz:
http://arxiv.org/abs/2404.04641
Autor:
Geng, Zhiyuan
We prove the uniqueness of $L^1$ blow-down limit at infinity for an entire minimizing solution $u:\mathbb{R}^2\rightarrow\mathbb{R}^2$ of a planar Allen-Cahn system with a triple-well potential. Consequently, $u$ can be approximated by a triple junct
Externí odkaz:
http://arxiv.org/abs/2404.02859
Autor:
Salib, Anthony, Weiss, Georg
Global solutions to the obstacle problem were first completely classified in two dimensions by Sakai using complex analysis techniques. Although the complex analysis approach produced a very succinct proof in two dimensions, it left the higher dimens
Externí odkaz:
http://arxiv.org/abs/2403.18879