Existence of solutions for a class of singular elliptic systems with convection term [PDF]
arXiv, 2013 We show the existence of positive solutions for a class of singular elliptic systems with convection term. The approach combines pseudomonotone operator theory, sub and supersolution method and perturbation arguments involving singular terms.
arxiv
Analysis of positive solutions for classes of quasilinear singular problems on exterior domains
Advances in Nonlinear Analysis, 2017 We consider the ...
Chhetri Maya +2 more
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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
Advanced Nonlinear Studies, 2017 In the present paper we study the Dirichlet problem for an equation involving the 1-Laplacian and a total variation term as reaction.We prove a strong multiplicity result.
Abdellaoui Boumediene +2 more
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$p$-Laplace equations with singular weights [PDF]
arXiv, 2013 We study a class of $p$-Laplacian Dirichlet problems with weights that are possibly singular on the boundary of the domain, and obtain nontrivial solutions using Morse theory. In the absence of a direct sum decomposition, we use a cohomological local splitting to get an estimate of the critical groups.
arxiv
On the moving plane method for boundary blow-up solutions to semilinear elliptic equations
Advances in Nonlinear Analysis, 2018 We consider weak solutions to -Δu=f(u){-\Delta u=f(u)} on Ω1∖Ω0{\Omega_{1}\setminus\Omega_{0}}, with u=c≥0{u=c\geq 0} in ∂Ω1{\partial\Omega_{1}} and u=+∞{u=+\infty} on ∂Ω0{\partial\Omega_{0}}, and we prove monotonicity properties of the solutions via
Canino Annamaria +2 more
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Unique continuation properties for relativistic Schrödinger operators with a singular potential [PDF]
arXiv, 2013 Asymptotics of solutions to relativistic fractional elliptic equations with Hardy type potentials is established in this paper. As a consequence, unique continuation properties are obtained.
arxiv
Ergodic pairs for degenerate pseudo Pucci's fully nonlinear operators [PDF]
arXiv, 2020 We study the ergodic problem for fully nonlinear elliptic operators $F( \nabla u, D^2 u)$ which may be degenerate when at least one of the components of the gradient vanishes. We extend here the results in the celebrated paper of Lasry and Lions, the ones of Leonori and Porretta Capuzzo Dolcetta Leoni and Porretta, Birindelli et al.
arxiv
Sharp essential self-adjointness of relativistic Schrödinger operators with a singular potential [PDF]
arXiv, 2014 This paper is devoted to the study of essential self-adjointness of a relativistic Schr\"{o}dinger operator with a singular homogeneous potential. From an explicit condition on the coefficient of the singular term, we provide a sufficient and necessary condition for essential self-adjointness.
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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