Results 41 to 50 of about 648 (60)

Strong Maximum Principle for Some Quasilinear Dirichlet Problems Having Natural Growth Terms

Advanced Nonlinear Studies, 2020
In this paper, dedicated to Laurent Veron, we prove that the Strong Maximum Principle holds for solutions of some quasilinear elliptic equations having lower order terms with quadratic growth with respect to the gradient of the solution.
Boccardo Lucio, Orsina Luigi
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Existence results of positive solutions for Kirchhoff type equations via bifurcation methods

, 2017
In this paper we address the following Kirchhoff type problem \begin{equation*} \left\{ \begin{array}{ll} -\Delta(g(|\nabla u|_2^2) u + u^r) = a u + b u^p& \mbox{in}~\Omega, u>0& \mbox{in}~\Omega, u= 0& \mbox{on}~\partial\Omega, \end{array} \right.
Cintra, Willian, Júnior, João R. Santos, Siciliano, Gaetano, Suárez, Antonio   +3 more
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The Gelfand problem for the 1-homogeneous p-Laplacian

Advances in Nonlinear Analysis, 2017
In this paper, we study the existence of viscosity solutions to the Gelfand problem for the 1-homogeneous p-Laplacian in a bounded domain Ω⊂ℝN{\Omega\subset\mathbb{R}^{N}}, that is, we deal ...
Carmona Tapia José, Molino Salas Alexis, Rossi Julio D.   +2 more
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Beyond the classical strong maximum principle: Sign-changing forcing term and flat solutions

Advances in Nonlinear Analysis
We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain can be extended, under suitable conditions, to the case in which the forcing term is sign ...
Díaz Jesús Ildefonso, Hernández Jesús   +1 more
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Regular Versus Singular Solutions in a Quasilinear Indefinite Problem with an Asymptotically Linear Potential

Advanced Nonlinear Studies, 2020
The aim of this paper is analyzing the positive solutions of the quasilinear ...
López-Gómez Julián, Omari Pierpaolo
doaj   +1 more source

Existence, uniqueness, localization and minimization property of positive solutions for non-local problems involving discontinuous Kirchhoff functions

Advances in Nonlinear Analysis
Let Ω⊂Rn\Omega \subset {{\bf{R}}}^{n} be a smooth bounded domain. In this article, we prove a result of which the following is a by-product: Let q∈]0,1[q\in ]0,1{[}, α∈L∞(Ω)\alpha \in {L}^{\infty }\left(\Omega ), with α>0\alpha \gt 0, and k∈Nk\in {\bf{N}}
Ricceri Biagio
doaj   +1 more source

Normalized solutions for Sobolev critical fractional Schrödinger equation

Advances in Nonlinear Analysis
In the present study, we investigate the existence of the normalized solutions to Sobolev critical fractional Schrödinger equation: (−Δ)su+λu=f(u)+∣u∣2s*−2u,inRN,(Pm)∫RN∣u∣2dx=m2,\hspace{14em}\left\{\begin{array}{ll}{\left(-\Delta )}^{s}u+\lambda u=f ...
Li Quanqing, Nie Jianjun, Wang Wenbo, Zhou Jianwen   +3 more
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Nonexistence of positive radial solutions for a problem with singular potential

Advances in Nonlinear Analysis, 2014
This article completes the picture in the study of positive radial solutions in the function space 𝒟1,2(ℝN)∩L2(ℝN,|x|-αdx)∩Lp(ℝN)${{\mathcal {D}^{1,2}({\mathbb {R}^N}) \cap L^2({{\mathbb {R}^N}, | x |^{-\alpha } dx})\cap L^p({\mathbb {R}^N})}}$ for the ...
Catrina Florin
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Sharp asymptotic expansions of entire large solutions to a class of k-Hessian equations with weights

Advances in Nonlinear Analysis
It is well-known that it is a quite interesting topic to study the asymptotic expansions of entire large solutions of nonlinear elliptic equations near infinity. But very little is done.
Wan Haitao
doaj   +1 more source

The strong maximum principle for Schrödinger operators on fractals

Demonstratio Mathematica, 2019
We prove a strong maximum principle for Schrödinger operators defined on a class of postcritically finite fractal sets and their blowups without boundary.
Ionescu Marius V., Okoudjou Kasso A., Rogers Luke G.   +2 more
doaj   +1 more source