Results 41 to 50 of about 604 (96)
, 2020 In this paper we address questions on the existence and multiplicity of solutions to the nonlinear elliptic system in divergence form ⎧⎨ ⎩ div (H∇u) = Hs|∇u|u+[cof∇u]∇P in Ω, det∇u = 1 in Ω, u = φ on ∂Ω.
George Morrison, A. Taheri
semanticscholar +1 more source
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
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Ground states and multiple solutions for Hamiltonian elliptic system with gradient term
Advances in Nonlinear Analysis, 2020 This paper is concerned with the following nonlinear Hamiltonian elliptic system with gradient ...
Zhang Wen, Zhang Jian, Mi Heilong
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A Fibering Map Approach for a Laplacian System With Sign-Changing Weight Function [PDF]
, 2014 We prove the existence of at least two positive solutions for the Laplacian system(E?)On a bounded region by using the Nehari manifold and the fibering maps associated with the Euler functional for the ...
Kazemipoor, Seyyed Sadegh +1 more
core
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
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Advances in Nonlinear AnalysisWe 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
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The Dirac equation without spinors
, 1998 In the first part of the paper we give a tensor version of the Dirac equation. In the second part we formulate and analyse a simple model equation which for weak external fields appears to have properties similar to those of the 2--dimensional Dirac ...
A Sudbery +8 more
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The Interaction Between PDE and Graphs in Multiscale Modeling
, 2016 In this article an upscaled model is presented, for complex networks with highly clustered regions exchanging some abstract quantities in both, microscale and macroscale level.
Morales, Fernando A +1 more
core +2 more sources
Multiplicity of semiclassical solutions for a class of nonlinear Hamiltonian elliptic system
Advances in Nonlinear AnalysisThis 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
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The Brezis–Nirenberg problem for nonlocal systems
Advances in Nonlinear Analysis, 2016 By means of variational methods we investigate existence, nonexistence as well as regularity of weak solutions for a system of nonlocal equations involving the fractional laplacian operator and with nonlinearity reaching the critical growth and ...
Faria Luiz F. O. +4 more
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