Results 61 to 70 of about 655 (93)

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

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

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

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

Hardy-Poincare' inequalities with boundary singularities [PDF]

arXiv, 2010
Let $\O$ be a bounded domain in $\R^N$ with $0\in\de\O$ and $N\ge 2$. In this paper we study the Hardy-Poincar\'e inequality for maps in $H^1_0(\Omega)$. In particular we give sufficient and some necessary conditions so that the best constant is achieved.
arxiv  

Exact behavior around isolated singularity for semilinear elliptic equations with a log-type nonlinearity

Advances in Nonlinear Analysis, 2018
We study the semilinear elliptic ...
Ghergu Marius, Kim Sunghan, Shahgholian Henrik   +2 more
doaj   +1 more source

Solutions to nonlinear Schrödinger equations with singular electromagnetic potential and critical exponent [PDF]

arXiv, 2010
We investigate existence and qualitative behaviour of solutions to nonlinear Schr\"odinger equations with critical exponent and singular electromagnetic potentials. We are concerned with magnetic vector potentials which are homogeneous of degree -1, including the Aharonov-Bohm class.
arxiv  

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

Uniqueness of solutions to singular p-Laplacian equations with subcritical nonlinearity

Advances in Nonlinear Analysis, 2017
We present a geometric approach to the study of quasilinear elliptic p-Laplacian problems on a ball in ℝn${\mathbb{R}^{n}}$ using techniques from dynamical systems.
Maultsby Bevin
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