Results 31 to 40 of about 76 (75)

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

Ergodic pairs for singular or degenerate fully nonlinear operatorsMathematical Subject Classification : 35J70, 35J75

, 2019
We study the ergodic problem for fully nonlinear operators which may be singular or degenerate when the gradient of solutions vanishes. We prove the convergence of both explosive solutions and solutions of Dirichlet problems for approximating equations.
Birindelli, Isabeau, Demengel, Françoise, Leoni, Fabiana   +2 more
openaire   +1 more source

Dirichlet problems for fully nonlinear equations with ”subquadratic” HamiltoniansMathematical Subject Classification : 35J70, 35J75

, 2019
For a class of fully nonlinear equations having second order operators which may be singular or degenerate when the gradient of the solutions vanishes, and having first order terms with power growth, we prove the existence and uniqueness of suitably defined viscosity solution of Dirichlet problem and we further show that it is a Lipschitz continuous ...
Birindelli, Isabeau, Demengel, Françoise, Leoni, Fabiana   +2 more
openaire   +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

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

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

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

Global multiplicity of solutions for a class of singular p-Laplacian equations

Demonstratio Mathematica
This paper is concerned with a singular problem involving a quasilinear operator and the critical term. We get the global existence and multiplicity of solutions as the parameter λ varies.
Tan Xiaoqing, Wang Libo
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