Nondegeneracy of positive solutions to nonlinear Hardy-Sobolev equations [PDF]
arXiv, 2016 In this note, we prove that the kernel of the linearized equation around a positive energy solution in $\mathbb{R}^n$, $n\geq 3$, to $-\Delta W-\gamma|x|^{-2}V=|x|^{-s}W^{2^\star(s)-1}$ is one-dimensional when $s+\gamma>0$. Here, $s\in [0,2)$, $0\leq\gamma<(n-2)^2/4$ and $2^\star(s)=2(n-s)/(n-2)$.
arxiv
Regularity for critical fractional Choquard equation with singular potential and its applications
Advances in Nonlinear AnalysisWe study the following fractional Choquard equation (−Δ)su+u∣x∣θ=(Iα*F(u))f(u),x∈RN,{\left(-\Delta )}^{s}u+\frac{u}{{| x| }^{\theta }}=({I}_{\alpha }* F\left(u))f\left(u),\hspace{1em}x\in {{\mathbb{R}}}^{N}, where N⩾3N\geqslant 3, s∈12,1s\in \left ...
Liu Senli, Yang Jie, Su Yu
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Liouville's type results for singular anisotropic operators
Analysis and Geometry in Metric SpacesWe present two Liouville-type results for solutions to anisotropic elliptic equations that have a growth of power 2 along the first ss coordinate directions and of power pp, with ...
Maria Cassanello Filippo +2 more
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Existence and a priori estimates of solutions for quasilinear singular elliptic systems with variable exponents [PDF]
arXiv, 2017 This article sets forth results on the existence, a priori estimates and boundedness of positive solutions of a singular quasilinear systems of elliptic equations involving variable exponents. The approach is based on Schauder's fixed point Theorem.
arxiv
On a nonlinear Robin problem with an absorption term on the boundary and L1 data
Advances in Nonlinear AnalysisWe deal with existence and uniqueness of nonnegative solutions to: −Δu=f(x),inΩ,∂u∂ν+λ(x)u=g(x)uη,on∂Ω,\left\{\begin{array}{ll}-\Delta u=f\left(x),\hspace{1.0em}& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\\ \frac{\partial u}{\partial ...
Pietra Francesco Della +2 more
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On Lane–Emden Systems with Singular Nonlinearities and Applications to MEMS
Advanced Nonlinear Studies, 2018 In this paper we analyze the Lane–Emden ...
do Ó João Marcos, Clemente Rodrigo
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(Non)uniqueness of minimizers in the least gradient problem [PDF]
arXiv, 2017 Minimizers in the least gradient problem with discontinuous boundary data need not be unique. However, all of them have a similar structure of level sets. Here, we give a full characterization of the set of minimizers in terms of any one of them and discuss stability properties of an approximate problem.
arxiv
Ireneo Peral: Forty Years as Mentor
Advanced Nonlinear Studies, 2017 In this article we present a survey of the Ph.D. theses that have been completed under the advice of Ireneo Peral.Following a chronological order, we summarize the main results contained in the works of the former students of Ireneo Peral.
Abdellaoui Boumediene +9 more
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A Liouville theorem for fully nonlinear problems with infinite boundary conditions and applications [PDF]
arXiv, 2019 We prove a Liouville type classification theorem in half-spaces for infinite boundary value problems related to fully nonlinear, uniformly elliptic operators. We then apply the result in order to obtain gradient boundary blow up rates for ergodic functions in bounded domains related to degenerate/singular operators, and, as a further consequence, we ...
arxiv
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