Results 51 to 60 of about 159 (128)

Blow-up solutions for a 4-dimensional semilinear elliptic system of Liouville type in some general cases

Boundary Value Problems
This paper is devoted to the existence of singular limit solutions for a nonlinear elliptic system of Liouville type under Navier boundary conditions in a bounded open domain of R 4 $\mathbb{R}^{4}$ .
Sami Baraket, Anis Ben Ghorbal, Rima Chetouane, Azedine Grine   +3 more
doaj   +1 more source

Ground State Solutions for General Choquard Equation With the Riesz Fractional Laplacian

Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.
In this work, we study the existence of a nonzero solution for the following nonlinear general Choquard equation (CE): −Δν+ν=−ΔD−α2 ∗ Fνfν,in ℝN, where N ≥ 3, F represents the primitive function of f, f∈CR;R is a function that fulfils the general Berestycki–Lions conditions, ΔD denotes the Laplacian operator on Ω with zero Dirichlet boundary conditions
Sarah Abdullah Qadha, Muneera Abdullah Qadha, Haibo Chen, Yuying Zao, Kang-Jia Wang   +4 more
wiley   +1 more source

Ground state solutions for a class of Schrödinger–Poisson–Slater equation with Coulomb–Sobolev critical exponent

Boundary Value Problems
This paper is concerned with the Schrödinger–Poisson–Slater equation involving the Coulomb–Sobolev exponent. We apply the concentration compactness principle and the Pohožaev-type identity to overcome loss of compactness caused by the Coulomb exponent ...
Jingai Du, Pengfei He, Hongmin Suo
doaj   +1 more source

Existence of Solutions for a Nonlinear Dirichlet Problem Involving Gradient Dependent Lipschitz Convection Function

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this paper, our goal is to prove the existence of a weak solution (in H01Ω) for a fully nonlinear Dirichlet problem with a nonmonotone (e.g., Lipschitz) convection function F that depends on ∇u, and a nonlinearity G that is not necessarily monotone and depends on the solution function u, and the higher order term is −ΔΓ(x, u) − diva(x, u, ∇u ...
Teffera M. Asfaw, Anteneh T. Adimasu, Achamyelesh A. Aligaz, Pramita Mishra   +3 more
wiley   +1 more source

The Calogero–Moser derivative nonlinear Schrödinger equation

Communications on Pure and Applied Mathematics, Volume 77, Issue 10, Page 4008-4062, October 2024.
Abstract We study the Calogero–Moser derivative nonlinear Schrödinger NLS equation i∂tu+∂xxu+(D+|D|)(|u|2)u=0$$\begin{equation*} i\partial _t u +\partial _{xx} u + (D+|D|)(|u|^2) u =0 \end{equation*}$$posed on the Hardy–Sobolev space H+s(R)$H^s_+(\mathbb {R})$ with suitable s>0$s>0$.
Patrick Gérard, Enno Lenzmann
wiley   +1 more source

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

The Pohozaev-Schoen Identity on Asymptotically Euclidean Manifolds: Conservation Identities and their applications

, 2020
The aim of this paper is to present a version of the generalized Pohozaev-Schoen identity in the context of asymptotically euclidean manifolds. Since these kind of geometric identities have proven to be a very powerful tool when analysing different geometric problems for compact manifolds, we will present a variety of applications within this new ...
Freitas, Allan, Ávalos, Rodrigo
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

Reverse Stein–Weiss Inequalities on the Upper Half Space and the Existence of Their Extremals

Advanced Nonlinear Studies, 2019
The purpose of this paper is four-fold. First, we employ the reverse weighted Hardy inequality in the form of high dimensions to establish the following reverse Stein–Weiss inequality on the upper half space:
Chen Lu, Lu Guozhen, Tao Chunxia
doaj   +1 more source