Results 51 to 60 of about 1,698 (113)

On a class of semilinear elliptic problems near critical growth

International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 2, Page 321-330, 1998., 1997
We use Minimax Methods and explore compact embedddings in the context of Orlicz and Orlicz‐Sobolev spaces to get existence of weak solutions on a class of semilinear elliptic equations with nonlinearities near critical growth. We consider both biharmonic equations with Navier boundary conditions and Laplacian equations with Dirichlet boundary ...
J. V. Goncalves, S. Meira
wiley   +1 more source

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

Weighted Sobolev spaces and ground state solutions for quasilinear elliptic problems with unbounded and decaying potentials

, 2013
In this paper, we prove some continuous and compact embedding theorems for weighted Sobolev spaces, and consider both a general framework and spaces of radially symmetric functions.
Guoqing Zhang
semanticscholar   +1 more source

Multiple solutions for a problem with resonance involving the p‐Laplacian

Abstract and Applied Analysis, Volume 3, Issue 1-2, Page 191-201, 1998., 1998
In this paper we will investigate the existence of multiple solutions for the problem where Δpu = div(|∇u|p−2∇u) is the p‐Laplacian operator, Ω⫅ℝN is a bounded domain with smooth boundary, h and g are bounded functions, N ≥ 1 and 1 < p < ∞. Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least ...
C. O. Alves, P. C. Carrião, O. H. Miyagaki   +2 more
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

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

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 of solitary waves in dipolar quantum gases

, 2010
We study a nonlinear Schroedinger equation arising in the mean-field description of dipolar quantum gases. Under the assumption of sufficiently strong dipolar interactions, the existence of standing waves, and hence solitons, is proved together with some
Antonelli, Paolo, Sparber, Christof
core   +1 more source