Results 61 to 70 of about 472 (105)

Existence of solutions for the coupled systems of second and fourth order elliptic equations

, 2011
In this paper, under the nonquadraticity condition, we obtain two existence theorems of nontrivial solutions for a coupled system of second and fourth order elliptic equations. Mathematics subject classification (2010): 35J48, 35J50, 35J58.
Lei Ji, Chunlei Tang
semanticscholar   +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

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

Optimal control for cooperative systems involving fractional Laplace operators

Journal of Inequalities and Applications, 2021
In this work, the elliptic 2 × 2 $2\times 2$ cooperative systems involving fractional Laplace operators are studied. Due to the nonlocality of the fractional Laplace operator, we reformulate the problem into a local problem by an extension problem. Then,
H. M. Serag, Abd-Allah Hyder, M. El-Badawy   +2 more
doaj   +1 more source

Strongly indefinite systems with critical Sobolev exponents

, 1998
We consider an elliptic system of Hamiltonian type on a bounded domain. In the superlinear case with critical growth rates we obtain existence and positivity results for solutions under suitable conditions on the linear terms.
J. Hulshof, E. Mitidieri, R. Vandervorst
semanticscholar   +1 more source

Ground State Solutions for the Nonlinear Schrödinger–Bopp–Podolsky System with Critical Sobolev Exponent

Advanced Nonlinear Studies, 2020
In this paper, we study the existence of ground state solutions for the nonlinear Schrödinger–Bopp–Podolsky system with critical Sobolev ...
Li Lin, Pucci Patrizia, Tang Xianhua
doaj   +1 more source

Regular solutions of elliptic boundary-value problems with discontinuous nonlinearities

, 2006
The existence of stable solutions to elliptic boundary-value problems is studied; stability is understood with respect to perturbations of nonlinearities.
M. Lepchinskiĭ, V. N. Pavlenko
semanticscholar   +1 more source

Ground state solutions for the nonlinear Klein-Gordon-Maxwell equations [PDF]

arXiv, 2008
In this paper we prove the existence of a ground state solution for the nonlinear Klein-Gordon-Maxwell equations in the electrostatic case.
arxiv  

A note on coupled nonlinear Schrödinger systems under the effect of general nonlinearities [PDF]

arXiv, 2009
We prove the existence of non-trivial solutions to a system of coupled, nonlinear, Schroedinger equations with general nonlinearity.
arxiv  

Multiple solutions for the quasilinear Choquard equation with Berestycki-Lions-type nonlinearities

Advances in Nonlinear Analysis
In this article, we study the following quasilinear equation with nonlocal nonlinearity −Δu−κuΔ(u2)+λu=(∣x∣−μ*F(u))f(u),inRN,-\Delta u-\kappa u\Delta \left({u}^{2})+\lambda u=\left({| x| }^{-\mu }* F\left(u))f\left(u),\hspace{1em}\hspace{0.1em}\text{in ...
Jia Yue, Yang Xianyong
doaj   +1 more source