Results 51 to 60 of about 500 (78)

On a fractional sublinear elliptic equation with a variable coefficient [PDF]

arXiv, 2013
We study existence and uniqueness of bounded solutions to a fractional sublinear elliptic equation with a variable coefficient, in the whole space. Existence is investigated in connection to a certain fractional linear equation, whereas the proof of uniqueness relies on uniqueness of solutions to an associated fractional porous medium equation with ...
arxiv  

Patterns with prescribed numbers of critical points on topological tori [PDF]

arXiv, 2020
We study the existence of critical points of stable stationary solutions to reaction-diffusion problems on topological tori. Stable nonconstant stationary solutions are often called patterns. We construct topological tori and patterns with prescribed numbers of critical points whose locations are explicit.
arxiv  

Nonexistence of positive radial solutions for a problem with singular potential

Advances in Nonlinear Analysis, 2014
This article completes the picture in the study of positive radial solutions in the function space 𝒟1,2(ℝN)∩L2(ℝN,|x|-αdx)∩Lp(ℝN)${{\mathcal {D}^{1,2}({\mathbb {R}^N}) \cap L^2({{\mathbb {R}^N}, | x |^{-\alpha } dx})\cap L^p({\mathbb {R}^N})}}$ for the ...
Catrina Florin
doaj   +1 more source

On Semilinear Elliptic Equation with Measurable Nonlinearity [PDF]

arXiv, 2013
We consider a semilinear elliptic equation in a bounded domain with zero boundary conditions. The nonlinearity is discontinuous and monotone, but it is not a Carath\'eodory's function. The existence theorem has been proved.
arxiv  

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

Limit profiles and uniqueness of ground states to the nonlinear Choquard equations

Advances in Nonlinear Analysis, 2018
Consider nonlinear Choquard ...
Seok Jinmyoung
doaj   +1 more source

Nonlinear Muckenhoupt-Wheeden type bounds on Reifenberg flat domains, with applications to quasilinear Riccati type equations [PDF]

arXiv, 2013
A weighted norm inequality of Muckenhoupt-Wheeden type is obtained for gradients of solutions to a class of quasilinear equations with measure data on Reifenberg flat domains. This essentially leads to a resolution of an existence problem for quasilinear Riccati type equations with a gradient source term of arbitrary power law growth.
arxiv  

Ground state solutions for a semilinear elliptic problem with critical-subcritical growth

Advances in Nonlinear Analysis, 2018
We prove the existence of at least one ground state solution for the semilinear elliptic ...
Alves Claudianor O., Ercole Grey, Huamán Bolaños M. Daniel   +2 more
doaj   +1 more source

Schrödinger-Poisson systems with a general critical nonlinearity [PDF]

arXiv, 2015
We consider a Schr\"odinger-Poisson system involving a general nonlinearity at critical growth and we prove the existence of positive solutions. The Ambrosetti-Rabinowitz condition is not required. We also study the asymptotics of solutions with respect to a parameter.
arxiv  

A Nonlocal Operator Breaking the Keller–Osserman Condition

Advanced Nonlinear Studies, 2017
This work is concerned about the existence of solutions to the nonlocal semilinear ...
Ferreira Raúl, Pérez-Llanos Mayte
doaj   +1 more source