Results 41 to 50 of about 95 (88)

Exact multiplicity of positive solutions to a superlinear problem

Electronic Journal of Differential Equations, 2003
We generalize previous uniqueness results on a semilinear elliptic equation with zero Dirichlet boundary condition and superlinear, subcritical nonlinearity.
Junping Shi
doaj  

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

Boundary charges and integral identities for solitons in (d+1)-dimensional field theories

Nuclear Physics B, 2017
We establish a 3-parameter family of integral identities to be used on a class of theories possessing solitons with spherical symmetry in d spatial dimensions.
Sven Bjarke Gudnason, Zhifeng Gao, Yisong Yang   +2 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

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

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

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

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