Results 141 to 150 of about 1,398 (233)

Uniqueness of Positive Solutions of Semilinear Elliptic Equations

Journal of Differential Equations, 1995
The uniqueness of positive solutions of the problem \[ \Delta u+ f(u)= 0, \quad u>0,\;x\in B_ R, \qquad u|_{\partial B_ R}=0, \] where \(f(u)\geq 0\), \(B_ R\) is a ball with radius \(R\) in \(\mathbb{R}^ n\), \(n>2\), is studied. The following nonlinearities \(f\) are considered: \(f(u)= u^ p+ u^ q\) and the more general case \(f(u)= \sum_{i=1}^ k a_ ...
openaire   +2 more sources

Positive solutions for semi-linear elliptic equations in exterior domains

Electronic Journal of Differential Equations, 2009
We prove the existence of a solution, decaying to zero at infinity, for the second order differential equation $$ frac{1}{A(t)}(A(t)u'(t))'+phi(t)+f(t,u(t))=0,quad tin (a,infty).
Habib Maagli, Sameh Turki, Noureddine Zeddini   +2 more
doaj  

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
doaj   +1 more source

Continuous Differentiability of the Value Function of Semilinear Parabolic Infinite Time Horizon Optimal Control Problems on L 2 ( Ω ) Under Control Constraints. [PDF]

Appl Math Optim, 2022
Kunisch K, Priyasad B.
europepmc   +1 more source

Uniqueness of positive solutions to a class of semilinear elliptic equations

Boundary Value Problems, 2011
In this article, we consider the uniqueness of positive radial solutions to the Dirichlet boundary value problem Δ u + f ( | x | , u ) + g ( | x | ) x ⋅ ∇ u = 0 , x ∈ Ω , u = 0 , x ∈ ∂ Ω ,
Li Chunming, Zhou Yong
doaj  

Semilinear equations in the plane with measurable data

Доповiдi Нацiональної академiї наук України
We study semilinear partial differential equations in the plane, the linear part of which is written in a divergence form. The main result is given as a factorization theorem.
V.Ya. Gutlyanskiĭ, O.V. Nesmelova, V.I. Ryazanov   +2 more
doaj   +1 more source

Solving Fredholm Integral Equations Using Deep Learning. [PDF]

Int J Appl Comput Math, 2022
Guan Y, Fang T, Zhang D, Jin C.
europepmc   +1 more source

Ground state solutions for semilinear elliptic equations with zero mass in R^N

Electronic Journal of Differential Equations, 2015
In this article, we study the semilinear elliptic equation $$\displaylines{ -\Delta u=|u|^{p(x)-2}u, \quad x\in \mathbb{R}^N\cr u\in D^{1,2}(\mathbb{R}^N), }$$ where $N\geq3$, $p(x)=\begin{cases} p, x\in\Omega\\ 2^*, x\not\in\Omega, \end ...
Jiu Liu, Jia-Feng Liao, Chun-Lei Tang
doaj  

Optimal control of stochastic partial differential equations in Banach spaces [PDF]

, 2010
In this thesis we study optimal control problems in Banach spaces for stochastic partial differential equations. We investigate two different approaches.
Serrano Perdomo, Rafael Antonio, o Perdomo, Rafael Antonio   +1 more
core  

Multiple nontrivial solutions of semilinear elliptic equations

, 1988
We give a condition for a semilinear elliptic equation to have two nontrivial solutions. Our condition does not demand any differentiability of the nonlinear term.
Norimichi Hirano
core   +1 more source