Results 1 to 10 of about 54,095 (261)

Infinitely many non-radial solutions for a Choquard equation

Advances in Nonlinear Analysis, 2022
In this article, we consider the non-linear Choquard equation −Δu+V(∣x∣)u=∫R3∣u(y)∣2∣x−y∣dyuinR3,-\Delta u+V\left(| x| )u=\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}\frac{| u(y){| }^{2}}{| x-y| }{\rm{d}}y\right)u\hspace{1.0em}\hspace{0.1em}\text{in}\
Gao Fashun, Yang Minbo
doaj   +3 more sources

Non-radial normalized solutions for a nonlinear Schrodinger equation

Electronic Journal of Differential Equations, 2023
This article concerns the existence of multiple non-radial positive solutions of the L²-constrained problem $$\displaylines{-\Delta{u}-Q(\varepsilon x)|u|^{p-2}u=\lambda{u},\quad \text{in }\mathbb{R}^N, \\ \int_{\mathbb{R}^N}|u|^2dx=1,}$$ where \(Q(x)\) is a radially symmetric function, ε>0 is a small parameter,
Zhi-Juan Tong, Jianqing Chen, Zhi-Qiang Wang   +2 more
doaj   +3 more sources

Radial and non-radial solutions for a nonlinear Schrodinger equation with a constraint

Electronic Journal of Differential Equations, 2021
We study the classical nonlinear Schodinger equation with a radially symmetric potential and a constraint, for the mass subcritical case. We obtain conditions that assure the existence of non-radial solutions. Also we show symmetry breaking of the ground states, and the existence of multiple non-radial solutions under additional conditions. Folr ...
Jiaxuan Yang, Yongqing Li, Zhi-Qiang Wang   +2 more
doaj   +2 more sources

Infinitely Many Radial and Non-Radial Solutions for a Class of Hemivariational Inequalities

Rocky Mountain Journal of Mathematics, 2005
This paper deals with the study of the following class of hemivariational inequalities: find \(u\in H^1(\mathbb R^N)\) such that \[ \int_{\mathbb R^N}(\nabla u\nabla w+uw)dx+\int_{\mathbb R^N}F^0_x(x,u(x);-w(x))dx\geq 0, \] for all \(w\in H^1(\mathbb R^N)\), where \(F^0\) stands for the generalized directional derivative in the sense of Clarke.
Alexandru Kristaly
exaly   +4 more sources

Infinitely many radial and non-radial solutions for a fractional Schrödinger equation

Computers and Mathematics With Applications, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xianhua Tang
exaly   +4 more sources

Non global solutions for non-radial inhomogeneous nonlinear Schrodinger equations

Electronic Journal of Differential Equations
This work concerns the inhomogeneous Schrodinger equation $$ \mathrm{i}\partial_t u-\mathcal{K}_{s,\lambda}u +F(x,u)=0 , \quad u(t,x):\mathbb{R}\times\mathbb{R}^N\to\mathbb{C}. $$ Here, $s\in\{1,2\}$, $N>2s$ and $\lambda>-(N-2)^2/4$.
Ruobing Bai, Tarek Saanouni
doaj   +2 more sources

Patterns of non-radial solutions to coupled semilinear elliptic systems on a disc [PDF]

Nonlinear Analysis, 2021
In this paper, we prove the existence of non-radial solutions to the problem $-\triangle u=f(z,u)$, $u|_{\partial D}=0$ on the unit disc $D:=\{z\in \mathbb C : |z|<1\}$ with $u(z)\in \mathbb R^k$, where $f$ is a sub-linear continuous function, differentiable with respect to $u$ at zero and satisfying $f(e^{iθ}z,u) = f(z,u)$ for all $θ\in \mathbb R$,
Balanov, Z., Hooton, E. (Edward), Krawcewicz, W., Rachinskii, D.   +3 more
openaire   +4 more sources

Infinitely many radial and non-radial sign-changing solutions for Schrödinger equations

Advances in Nonlinear Analysis, 2022
In the present paper, a class of Schrödinger equations is investigated, which can be stated as −Δu+V(x)u=f(u),    x∈ℝN.- \Delta u + V(x)u = f(u),\;\;\;\;x \in {{\rm{\mathbb R}}^N}.
Li Gui-Dong, Li Yong-Yong, Tang Chun-Lei
doaj   +1 more source

Non radial solutions for a non homogeneous Hénon equation [PDF]

Nonlinear Analysis: Theory, Methods & Applications, 2014
In this paper we study a Hénon-like equation (see equations (1) below), where the nonlinearity f(t) is not homogeneous (i.e., it is not a power). By minimization on the Nehari manifold, we prove that for large values of the parameter $α$ there is a breaking of symmetry and non radial solutions appears.
BADIALE, Marino, G. Cappa
openaire   +3 more sources

Existence of positive radial solutions to a p-Laplacian Kirchhoff type problem on the exterior of a ball [PDF]

Opuscula Mathematica, 2022
In this paper the authors study the existence of positive radial solutions to the Kirchhoff type problem involving the \(p\)-Laplacian \[-\Big(a+b\int_{\Omega_e}|\nabla u|^p dx\Big)\Delta_p u=\lambda f\left(|x|,u\right),\ x\in \Omega_e,\quad u=0\ \text ...
John R. Graef, Doudja Hebboul, Toufik Moussaoui   +2 more
doaj   +1 more source