Results 91 to 100 of about 186 (147)

A weak Harnack estimate for supersolutions to the porous medium equation

Differential and Integral Equations, 2017
In this work, we prove a weak Harnack estimate for the weak supersolutions to the porous medium equation. The proof is based on a priori estimates for the supersolutions and measure theoretical arguments.
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On the sub-supersolution method for \(p(x)\)-Laplacian equations

Journal of Mathematical Analysis and Applications, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Existence of positive solutions for p(x)-Laplacian equations with a singular nonlinear term

Electronic Journal of Differential Equations, 2014
In this article, we study the existence of positive solutions for the p(x)-Laplacian Dirichlet problem $$ -\Delta _{p(x)}u=\lambda f(x,u) $$ in a bounded domain $\Omega \subset \mathbb{R}^{N}$.
Jingjing Liu, Qihu Zhang, Chunshan Zhao
doaj  

Positive solutions for concave-convex type problems for the one-dimensional $\phi$-Laplacian

Electronic Journal of Qualitative Theory of Differential Equations
Let $\Omega=(a,b)\subset\mathbb{R}$, $0\leq m,n\in L^{1}(\Omega)$, $\lambda,\mu>0$ be real parameters, and $\phi: \mathbb{R}\rightarrow\mathbb{R}$ be an odd increasing homeomorphism.
Uriel Kaufmann, Leandro Milne
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Existence of large solutions for a semilinear elliptic problem via explosive sub- supersolutions

Electronic Journal of Differential Equations, 2006
We consider the boundary blow-up nonlinear elliptic problems $Delta upmlambda | abla u|^q=k(x)g(u)$ in a bounded domain with boundary condition $u|_{partial Omega}=+infty$, where $qin [0, 2]$ and $lambdageq0$. Under suitable growth assumptions on $k$
Zhijun Zhang
doaj  

Infinite semipositone problems with indefinite weight and asymptotically linear growth forcing-terms

Electronic Journal of Differential Equations, 2013
In this work, we study the existence of positive solutions to the singular problem $$displaylines{ -Delta_{p}u = lambda m(x)f(u)-u^{-alpha} quad hbox{in }Omega,cr u = 0 quad hbox{on }partial Omega, }$$ where $lambda$ is positive parameter, $Omega $
Ghasem A. Afrouzi, Saleh Shakeri
doaj  

Propagation of Epidemics Along Lines with Fast Diffusion. [PDF]

Bull Math Biol, 2020
Berestycki H, Roquejoffre JM, Rossi L.
europepmc   +1 more source

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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Subsolutions: A journey from positone to infinite semipositone problems

Electronic Journal of Differential Equations, 2009
We discuss the existence of positive solutions to $-Delta u=lambda f(u)$ in $Omega$, with $u=0$ on the boundary, where $lambda$ is a positive parameter, $Omega$ is a bounded domain with smooth boundary $Delta $ is the Laplacian operator, and $f:(0 ...
Eun Kyoung Lee, Ratnasingham Shivaji, Jinglong Ye   +2 more
doaj  

A free boundary approach to shape optimization problems. [PDF]

Philos Trans A Math Phys Eng Sci, 2015
Bucur D, Velichkov B.
europepmc   +1 more source