Absolute continuity of the best Sobolev constant of a bounded domain
, 2012 Let $\lambda_{q}:=\inf{\Vert\nabla u\Vert_{L^{p}(\Omega)}^{p}/\Vertu\Vert_{L^{q}(\Omega)}^{p}:u\in W_{0}^{1,p}(\Omega)\setminus{0}} $, where $\Omega$ is a bounded and smooth domain of $\mathbb{R}^{N ...
Antonietti +10 more
core +1 more source
The Neumann function and the L p Neumann problem in chord-arc domains
Advanced Nonlinear StudiesWe construct the Neumann function in a 1-sided chord-arc domain (i.e., a uniform domain with an Ahlfors regular boundary), and establish size and Hölder continuity estimates up to the boundary.
Hofmann Steve, Sparrius Derek
doaj +1 more source
Liouville Type Theorem For A Nonlinear Neumann Problem [PDF]
, 2016 Consider the following nonlinear Neumann problem \[ \begin{cases} \text{div}\left(y^{a}\nabla u(x,y)\right)=0, & \text{for }(x,y)\in\mathbb{R}_{+}^{n+1}\\ \lim_{y\rightarrow0+}y^{a}\frac{\partial u}{\partial y}=-f(u), & \text{on }\partial\mathbb{R}_ ...
Xiang, Changlin
core
Loop Type Subcontinua of Positive Solutions for Indefinite Concave-Convex Problems
Advanced Nonlinear Studies, 2019 We establish the existence of loop type subcontinua of nonnegative solutions for a class of concave-convex type elliptic equations with indefinite weights, under Dirichlet and Neumann boundary conditions.
Kaufmann Uriel +2 more
doaj +1 more source
Global Dynamics of Generalized Logistic Equations
Advanced Nonlinear Studies, 2018 We consider a parameter dependent parabolic logistic population model with diffusion and degenerate logistic term allowing for refuges for the population.
Daners Daniel, López-Gómez Julián
doaj +1 more source
Nonlinear Boundary Value Problems via Minimization on Orlicz-Sobolev Spaces [PDF]
, 2013 We develop arguments on convexity and minimization of energy functionals on Orlicz-Sobolev spaces to investigate existence of solution to the equation $\displaystyle -\mbox{div} (\phi(|\nabla u|) \nabla u) = f(x,u) + h \mbox{in} \Omega$ under Dirichlet ...
Carvalho, M. L. M., Goncalves, J. V.
core
Simulating accurate and effective solutions of some nonlinear nonlocal two-point BVPs: Clique and QLM-clique matrix methods. [PDF]
Heliyon, 2023 Izadi M, Singh J, Noeiaghdam S.
europepmc +1 more source
Ground state solution of a nonlocal boundary-value problem
, 2013 In this paper, we apply the method of the Nehari manifold to study the Kirchhoff type equation \begin{equation*} -\Big(a+b\int_\Omega|\nabla u|^2dx\Big)\Delta u=f(x,u) \end{equation*} submitted to Dirichlet boundary conditions.
Batkam, Cyril Joel
core +1 more source
On a nonlinear Robin problem with an absorption term on the boundary and L1 data
Advances in Nonlinear AnalysisWe deal with existence and uniqueness of nonnegative solutions to: −Δu=f(x),inΩ,∂u∂ν+λ(x)u=g(x)uη,on∂Ω,\left\{\begin{array}{ll}-\Delta u=f\left(x),\hspace{1.0em}& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\\ \frac{\partial u}{\partial ...
Pietra Francesco Della +2 more
doaj +1 more source
Convergence analysis for double phase obstacle problems with multivalued convection term
Advances in Nonlinear Analysis, 2020 In the present paper, we introduce a family of the approximating problems corresponding to an elliptic obstacle problem with a double phase phenomena and a multivalued reaction convection term.
Zeng Shengda +3 more
doaj +1 more source