Results 51 to 60 of about 1,690 (115)

Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities

Advanced Nonlinear Studies
In this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia, Gallo Marco, Tanaka Kazunaga   +2 more
doaj   +1 more source

Liouville Type Theorem For A Nonlinear Neumann Problem [PDF]

, 2016
Consider the following nonlinear Neumann problem \[ \begin{cases} \text{div}\left(y^{a}\nabla u(x,y)\right)=0, & \text{for }(x,y)\in\mathbb{R}_{+}^{n+1}\\ \lim_{y\rightarrow0+}y^{a}\frac{\partial u}{\partial y}=-f(u), & \text{on }\partial\mathbb{R}_ ...
Xiang, Changlin
core  

EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR NONLINEAR SCHRÖDINGER-KIRCHHOFF-TYPE EQUATIONS

, 2016
. In this paper, we consider the following Schro¨dinger-Kirch-hoff-type equationsa+ bZ R N (|∇u| 2 + V(x)|u| 2 )dx[−∆u+ V(x)u] = f(x,u), in R N .Under certain assumptions on V and f, some new criteria on the exis-tence and multiplicity of nontrivial ...
Haibo Chen, Hongliang Liu, Liping Xu
semanticscholar   +1 more source

On quasilinear elliptic equations in ℝN

Abstract and Applied Analysis, Volume 1, Issue 4, Page 407-415, 1996., 1996
In this note we give a result for the operator p‐Laplacian complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation −Δu = h(x)uq in ℝN, where 0 < q < 1, to have a bounded positive solution. While Brézis and Kamin use the method of sub and super solutions, we employ variational arguments for the ...
C. O. Alves, J. V. Concalves, L. A. Maia
wiley   +1 more source

Bifurcation and multiplicity results for critical problems involving the p-Grushin operator

Advances in Nonlinear Analysis
In this article, we prove a bifurcation and multiplicity result for a critical problem involving a degenerate nonlinear operator Δγp{\Delta }_{\gamma }^{p}. We extend to a generic p>1p\gt 1 a result, which was proved only when p=2p=2. When p≠2p\ne 2, the
Malanchini Paolo, Bisci Giovanni Molica, Secchi Simone   +2 more
doaj   +1 more source

Non-trivial solutions for Schrödinger-Poisson systems involving critical nonlocal term and potential vanishing at infinity

Open Mathematics, 2019
The present study is concerned with the following Schrödinger-Poisson system involving critical nonlocal ...
Shao Liuyang
doaj   +1 more source

A multiplicity result for the scalar field equation

, 2013
We prove the existence of $N - 1$ distinct pairs of nontrivial solutions of the scalar field equation in ${\mathbb R}^N$ under a slow decay condition on the potential near infinity, without any symmetry assumptions.
Perera, Kanishka
core   +1 more source

A weighted Hardy-type inequality for 0

, 2015
Hardy-type inequalities with sharp costants for 0 < p < 1 for power weight functions were established in [10], [5]. In this work, we give an extension of these inequalities for general weight functions, prove the existence of extremal functions and write
N. Azzouz, V. Burenkov, A. Senouci
semanticscholar   +1 more source

On certain nonlinear elliptic systems with indefinite terms

Electronic Journal of Differential Equations, 2002
We consider an elliptic quasi linear systems with indefinite term on a bounded domain. Under suitable conditions, existence and positivity results for solutions are given. Submitted April 2, 2002. Published October 2, 2002.
Ahmed Bensedik, Mohammed Bouchekif
doaj  

Infinitely many solutions for a class of Kirchhoff-type equations

Open Mathematics
In this article, we consider a class of Kirchhoff-type equations: −a+b∫Ω∣∇u∣2dxΔu=f(x,u),x∈Ω,u=0,x∈∂Ω.\left\{\begin{array}{ll}-\left(a+b\mathop{\displaystyle \int }\limits_{\Omega }{| \nabla u| }^{2}{\rm{d}}x\right)\Delta u=f\left(x,u),\hspace{1.0em}& x ...
Zhou Qin, Zeng Jing
doaj   +1 more source