Results 31 to 40 of about 564 (71)

Determination of AdS Monopole Wall via Minimization

, 2019
In this note we solve a minimization problem arising in a recent work of Bolognesi and Tong on the determination of an AdS monopole wall. We show that the problem has a unique solution. Although the solution cannot be obtained explicitly, we show that it
Cao, Lei, Yang, Yisong
core   +1 more source

Existence and multiplicity of solutions for a class of superlinear elliptic systems

Advances in Nonlinear Analysis, 2018
In this paper, we establish the existence and multiplicity of solutions for a class of superlinear elliptic systems without Ambrosetti and Rabinowitz growth condition. Our results are based on minimax methods in critical point theory.
Li Chun, Agarwal Ravi P., Wu Dong-Lun
doaj   +1 more source

On the existence and multiplicity of solutions to fractional Lane-Emden elliptic systems involving measures

Advances in Nonlinear Analysis, 2020
We study positive solutions to the fractional Lane-Emden ...
Bhakta Mousomi, Nguyen Phuoc-Tai
doaj   +1 more source

Groundstates of the Choquard equations with a sign-changing self-interaction potential

, 2018
We consider a nonlinear Choquard equation $$ -\Delta u+u= (V * |u|^p )|u|^{p-2}u \qquad \text{in }\mathbb{R}^N, $$ when the self-interaction potential $V$ is unbounded from below.
Battaglia, Luca, Van Schaftingen, Jean
core   +1 more source

Multiplicity of solutions for a nonhomogeneous quasilinear elliptic equation with concave-convex nonlinearities

Advances in Nonlinear Analysis
We investigate the multiplicity of solutions for a quasilinear scalar field equation with a nonhomogeneous differential operator defined bySu≔−divϕu2+∣∇u∣22∇u+ϕu2+∣∇u∣22u,Su:= -\hspace{0.1em}\text{div}\hspace{0.1em}\left\{\phi \left(\frac{{u}^{2 ...
Qi Wanting, Zhang Xingyong
doaj   +1 more source

Concentration behavior of semiclassical solutions for Hamiltonian elliptic system

Advances in Nonlinear Analysis, 2020
In this paper, we study the following nonlinear Hamiltonian elliptic system with gradient ...
Zhang Jian, Chen Jianhua, Li Quanqing, Zhang Wen   +3 more
doaj   +1 more source

Moser-Trudinger inequalities for singular Liouville systems

, 2015
In this paper we prove a Moser-Trudinger inequality for the Euler-Lagrange functional of a general singular Liouville system. We characterize the values of the parameters which yield coercivity for the functional and we give necessary conditions for ...
Battaglia, Luca
core   +1 more source

Multiplicity of semiclassical solutions for a class of nonlinear Hamiltonian elliptic system

Advances in Nonlinear Analysis
This article is concerned with the following Hamiltonian elliptic system: −ε2Δu+εb→⋅∇u+u+V(x)v=Hv(u,v)inRN,−ε2Δv−εb→⋅∇v+v+V(x)u=Hu(u,v)inRN,\left\{\begin{array}{l}-{\varepsilon }^{2}\Delta u+\varepsilon \overrightarrow{b}\cdot \nabla u+u+V\left(x)v={H}_ ...
Zhang Jian, Zhou Huitao, Mi Heilong
doaj   +1 more source

Sharp non-existence results of prescribed L^2-norm solutions for some class of Schr\"odinger-Poisson and quasilinear equations

, 2012
In this paper we study the existence of minimizers for $$ F(u) = \1/2\int_{\R^3} |\nabla u|^2 dx + 1/4\int_{\R^3}\int_{\R^3}\frac{| u(x) |^2| u(y) |^2}{| x-y |}dxdy-\frac{1}{p}\int_{\R^3}| u |^p dx$$ on the constraint $$S(c) = \{u \in H^1(\R^3) : \int_ ...
Jeanjean, Louis, Luo, Tingjian
core   +2 more sources

Normalized solutions of Kirchhoff equations with Hartree-type nonlinearity

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023
In the present paper, we prove the existence of the solutions (λ, u) ∈ ℝ × H1(ℝ3) to the following Kirchhoff equations with the Hartree-type nonlinearity under the general mass supercritical settings, {-(a+b∫ℝ3|∇u|2dx)Δu-λu=[Iα*(K(x)F(u))]K(x)f(u),u∈H1 ...
Yuan Shuai, Gao Yuning
doaj   +1 more source