Results 1 to 10 of about 741 (89)
Isolated Singularities of Polyharmonic Inequalities [PDF]
arXiv, 2010 We study nonnegative classical solutions $u$ of the polyharmonic inequality $-\Delta^m u > 0$ in a punctured neighborhood of the origin in $R^n$. We give necessary and sufficient conditions on integers $n\ge 2$ and $m\ge 1$ such that these solutions $u$ satisfy a pointwise a priori bound as $x\to 0$.
Ghergu, Marius +2 more
arxiv +4 more sources
The Dirichlet problem for fully nonlinear degenerate elliptic equations with a singular nonlinearity [PDF]
arXiv, 2019 We investigate the homogeneous Dirichlet problem in uniformly convex domains for a large class of degenerate elliptic equations with singular zero order term. In particular we establish sharp existence and uniqueness results of positive viscosity solutions.
Birindelli, Isabeau, Galise, Giulio
arxiv +3 more sources
On an evolution equation in sub-Finsler geometry [PDF]
Analysis and Geometry in Metric SpacesWe study the gradient flow of an energy with mixed homogeneity, which is at the interface of Finsler and sub-Riemannian geometry.
Garofalo Nicola
doaj +2 more sources
From Hardy to Rellich inequalities on graphs
Proceedings of the London Mathematical Society, Volume 122, Issue 3, Page 458-477, March 2021., 2021 Abstract We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality.
Matthias Keller +2 more
wiley +1 more source
Advanced Nonlinear Studies, 2023 We consider the existence and nonexistence of the positive solution for the following Brézis-Nirenberg problem with logarithmic perturbation: −Δu=∣u∣2∗−2u+λu+μulogu2x∈Ω,u=0x∈∂Ω,\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{ll}-\Delta u={| u| }^{{2}^
Deng Yinbin +3 more
doaj +1 more source
Advances in Nonlinear Analysis, 2022 In this paper we study the existence and the nonexistence of solutions to an inhomogeneous non-linear elliptic problem (P)−Δu+u=F(u)+κμ in RN, u>0 in RN, u(x)→0 as |x|→∞,- \Delta u + u = F(u) + \kappa \mu \quad {\kern 1pt} {\rm in}{\kern 1pt ...
Ishige Kazuhiro +2 more
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Monotonicity of solutions for fractional p-equations with a gradient term
Open Mathematics, 2022 In this paper, we consider the following fractional pp-equation with a gradient term: (−Δ)psu(x)=f(x,u(x),∇u(x)).{\left(-\Delta )}_{p}^{s}u\left(x)=f\left(x,u\left(x),\nabla u\left(x)). We first prove the uniqueness and monotonicity of positive solutions
Wang Pengyan
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Sign changing solutions of Poisson's equation
Proceedings of the London Mathematical Society, Volume 121, Issue 3, Page 513-536, September 2020., 2020 Abstract Let Ω be an open, possibly unbounded, set in Euclidean space Rm with boundary ∂Ω, let A be a measurable subset of Ω with measure |A| and let γ∈(0,1). We investigate whether the solution vΩ,A,γ of −Δv=γ1Ω∖A−(1−γ)1A with v=0 on ∂Ω changes sign. Bounds are obtained for |A| in terms of geometric characteristics of Ω (bottom of the spectrum of the ...
M. van den Berg, D. Bucur
wiley +1 more source
Positive solution for a nonlocal problem with strong singular nonlinearity
Open Mathematics, 2023 In this article, we consider a nonlocal problem with a strong singular term and a general weight function. By using Ekeland’s variational principle, we prove a necessary and sufficient condition for the existence of a positive solution.
Wang Yue +3 more
doaj +1 more source
Open Mathematics, 2021 In this study, we consider the following quasilinear Choquard equation with singularity −Δu+V(x)u−uΔu2+λ(Iα∗∣u∣p)∣u∣p−2u=K(x)u−γ,x∈RN,u>0,x∈RN,\left\{\begin{array}{ll}-\Delta u+V\left(x)u-u\Delta {u}^{2}+\lambda \left({I}_{\alpha }\ast | u{| }^{p})| u{| }
Shao Liuyang, Wang Yingmin
doaj +1 more source