Results 51 to 60 of about 160 (129)

Traveling waves for a nonlinear Schrödinger system with quadratic interaction in ℝ4$$ {\mathrm{\mathbb{R}}}^4 $$

Mathematical Methods in the Applied Sciences, Volume 47, Issue 15, Page 12121-12131, October 2024.
In this paper, we consider a nonlinear Schrödinger system with quadratic interaction. We extend the recent results of Fukaya et al. (Math. Ann. 2024) and show that the system has a ground state in ℝ4$$ {\mathrm{\mathbb{R}}}^4 $$ when the mass parameter κ$$ \kappa $$ is larger than 12$$ \frac{1}{2} $$.
Amin Esfahani
wiley   +1 more source

Pohozaev identities for anisotropic integro-differential operators

, 2015
We establish Pohozaev identities and integration by parts type formulas for anisotropic integro-differential operators of order 2s, with s ϵ (0, 1). These identities involve local boundary terms, in which the quantity u/ds ∂Ω plays the role that ∂u/∂v plays in the second order case.
Ros-Oton, Xavier, Serra, Joaquim, Valdinoci, Enrico   +2 more
openaire   +2 more sources

Least energy solutions for a class of (p1,p2)$(p_{1}, p_{2})$‐Kirchhoff‐type problems in RN$\mathbb {R}^{N}$ with general nonlinearities

Journal of the London Mathematical Society, Volume 110, Issue 4, October 2024.
Abstract We examine the following (p1,p2)$(p_{1}, p_{2})$‐Kirchhoff‐type problem: −M1∥∇u∥Lp1(RN)p1Δp1u−M2∥∇u∥Lp2(RN)p2Δp2u=g(u)inRN,u∈W1,p1(RN)∩W1,p2(RN),$$\begin{equation*} {\left\lbrace \def\eqcellsep{&}\begin{array}{ll}-M_{1}\left(\Vert \nabla u\Vert ^{p_{1}}_{L^{p_{1}}(\mathbb {R}^{N})}\right)\Delta _{p_{1}}u-M_{2}\left(\Vert \nabla u\Vert ^{p_{2 ...
Vincenzo Ambrosio
wiley   +1 more source

Boundary Regularity, Pohozaev Identities and Nonexistence Results

, 2017
In this expository paper we survey some recent results on Dirichlet problems of the form $Lu=f(x,u)$ in $Ω$, $u\equiv0$ in $\mathbb R^n\backslashΩ$. We first discuss in detail the boundary regularity of solutions, stating the main known results of Grubb and of the author and Serra. We also give a simplified proof of one of such results, focusing on the
openaire   +2 more sources

Overdetermined boundary value problems with strongly nonlinear elliptic PDE

Electronic Journal of Qualitative Theory of Differential Equations, 2012
We consider the strongly nonlinear elliptic Dirichlet problem in a connected bounded domain, overdetermined with the constant Neumann condition $F(\nabla u)=c$ on the boundary. Here $F$ is convex and positively homogeneous of degree 1, and its polar $F^
Boqiang Lv, Fengquan Li, Weilin Zou
doaj   +1 more source

Integrability of Einstein deformations and desingularizations

Communications on Pure and Applied Mathematics, Volume 77, Issue 1, Page 177-220, January 2024.
Abstract We study the question of the integrability of Einstein deformations and relate it to the question of the desingularization of Einstein metrics. Our main application is a negative answer to the long‐standing question of whether or not every Einstein 4‐orbifold (which is an Einstein metric space in a synthetic sense) is limit of smooth Einstein ...
Tristan Ozuch
wiley   +1 more source

A Pohozaev Identity on Warped Product Solitons

, 2016
Warped product metrics are a class of Riemannian metrics on cross products $B \times F$ which have been well studied and provide a rich set of examples. In this paper we consider shrinking gradient Ricci solitons which are warped product metrics. We prove that if the curvature of the metric is bounded and the base $B$ has two dimensions, the metric ...
openaire   +2 more sources

Uniqueness for a semilinear elliptic equation in non-contractive domains under supercritical growth conditions

Electronic Journal of Differential Equations, 1999
We apply the Pohozaev identity to sub-domains of a tubular neighbourhood of a closed or broken curve in $Bbb R^n$ and establish uniqueness results for the smooth solutions of the Dirichlet problem for $-Delta u+|u|^{p-1}u=0$.
Kewei Zhang
doaj  

Nondegeneracy of the solutions for elliptic problem with critical exponent

Boundary Value Problems
This paper deals with the following nonlinear elliptic equation: − Δ u = Q ( | y ′ | , y ″ ) u N + 2 N − 2 , u > 0 , in R N , u ∈ D 1 , 2 ( R N ) , $$ -\Delta u=Q(|y'|,y'')u^{\frac{N+2}{N-2}},\,\,u>0,\,\,\text{in}\,{ \mathbb{R}}^{N},\,\,u\in D^{1,2 ...
Qingfang Wang
doaj   +1 more source

Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations

Communications on Pure and Applied Mathematics, Volume 77, Issue 1, Page 3-36, January 2024.
Abstract We consider finite Morse index solutions to semilinear elliptic questions, and we investigate their smoothness. It is well‐known that: ‐For n=2$n=2$, there exist Morse index 1 solutions whose L∞$L^\infty$ norm goes to infinity. ‐For n≥3$n \ge 3$, uniform boundedness holds in the subcritical case for power‐type nonlinearities, while for ...
Alessio Figalli, Yi Ru‐Ya Zhang
wiley   +1 more source