Results 31 to 40 of about 78 (75)

Existence results for some anisotropic possible singular problems via the sub-supersolution method

Using the sub-super solution method, we prove the existence of the solutions for the following anisotropic problem with singularity, where Ω⊂RN is a bounded domain with smooth boundary and a given singular nonlinearity f : Ω×(0,∞)⟶[0,∞) f : Ω×(0,∞)⟶[0,∞).
FOUAD, Kissi, EL AMROUSS, Abdelrachid, ABDELLAH, Hamidi   +2 more
core   +1 more source

A-priori Estimates Near the Boundary for Solutions of a class of Degenerate Elliptic Problems in Besov-type Spaces

Moroccan Journal of Pure and Applied Analysis, 2017
In this paper, we give a priori estimates near the boundary for solutions of a degenerate elliptic problems in the general Besov-type spaces Bp,qs,τ$B_{p,q}^{s,\tau }$, containing as special cases: Goldberg space bmo, local Morrey-Campanato spaces l2,λ ...
El Baraka Azzeddine, Masrour Mohammed
doaj   +1 more source

Up-to-Boundary Pointwise Gradient Estimates for Very Singular Quasilinear Elliptic Equations with Mixed Data

Advanced Nonlinear Studies, 2021
This paper establishes pointwise estimates up to boundary for the gradient of weak solutions to a class of very singular quasilinear elliptic equations with mixed ...
Do Tan Duc, Truong Le Xuan, Trong Nguyen Ngoc   +2 more
doaj   +1 more source

Neumann problem with a discontinuous nonlinearity

Demonstratio Mathematica
This study is devoted to proving the existence of weak solutions for a nonlinear elliptic problem with Neumann-type boundary data. The problem is driven by a discontinuous power nonlinearity and a nonsmooth prescribed data. Additionally, we aim to derive
Choudhuri Debajyoti, Repovš Dušan D., Saoudi Kamel   +2 more
doaj   +1 more source

Multiplicity of k-convex solutions for a singular k-Hessian system

Demonstratio Mathematica
In this article, we study the following nonlinear kk-Hessian system with singular weights Sk1k(σ(D2u1))=λb(∣x∣)f(−u1,−u2),inΩ,Sk1k(σ(D2u2))=λh(∣x∣)g(−u1,−u2),inΩ,u1=u2=0,on∂Ω,\left\{\begin{array}{ll}{S}_{k}^{\frac{1}{k}}(\sigma ({D}^{2}{u}_{1}))=\lambda ...
Yang Zedong, Bai Zhanbing
doaj   +1 more source

The trace space of anisotropic least gradient functions depends on the anisotropy. [PDF]

Math Ann, 2023
Górny W.
europepmc   +1 more source

Nondegeneracy of positive solutions to nonlinear Hardy–Sobolev equations

Advances in Nonlinear Analysis, 2017
In this note, we prove that the kernel of the linearized equation around a positive energy solution in ℝn${\mathbb{R}^{n}}$, n≥3${n\geq 3}$, to the problem -Δ⁢W-γ⁢|x|-2⁢V=|x|-s⁢W2⋆⁢(s)-1$-\Delta W-\gamma|x|^{-2}V=|x|^{-s}W^{2^{\star}(s)-1}$ is one ...
Robert Frédéric
doaj   +1 more source

Elliptic Equations with Hardy Potential and Gradient-Dependent Nonlinearity

Advanced Nonlinear Studies, 2020
Let Ω⊂ℝN{\Omega\subset\mathbb{R}^{N}} (N≥3{N\geq 3}) be a C2{C^{2}} bounded domain, and let δ be the distance to ∂⁡Ω{\partial\Omega}. We study equations (E±){(E_{\pm})}, -Lμ⁢u±g⁢(u,|∇⁡u|)=0{-L_{\mu}u\pm g(u,\lvert\nabla u\rvert)=0} in Ω, where Lμ=Δ+μδ2 ...
Gkikas Konstantinos T., Nguyen Phuoc-Tai
doaj   +1 more source

Nontrivial solutions for singular semilinear elliptic equations on the Heisenberg group

Advances in Nonlinear Analysis, 2014
In this article, we prove the existence of nontrivial weak solutions to the singular boundary value problem -Δℍnu=μg(ξ)u(|z|4+t2)12+λf(ξ,u)$-\Delta _{{\mathbb {H}}^{n}} u= \mu \frac{g(\xi ) u}{(|z|^{4}+ t^{2} )^{\frac{1}{2} }} +\lambda f(\xi , u)$ in Ω ...
Tyagi Jagmohan
doaj   +1 more source

On Cauchy–Liouville-type theorems

Advances in Nonlinear Analysis, 2017
In this paper we explore Liouville-type theorems to solutions of PDEs involving the ϕ-Laplace operator in the setting of Orlicz–Sobolev spaces. Our results extend Liouville-type theorems that have been obtained recently.
Araya Ataklti, Mohammed Ahmed
doaj   +1 more source