Results 51 to 60 of about 75,181 (273)

Some maximum principles for solutions of a class of partial differential equations in Ω⊂ℝn

International Journal of Mathematics and Mathematical Sciences, 2000
We find maximum principles for solutions of semilinear elliptic partial differential equations of the forms: (1) Δ2u+αf(u)=0, α∈ℝ+ and (2) ΔΔu+α(Δu)k+gu=0, α≤0 in some region Ω⊂ℝn.
Mohammad Mujalli Al-Mahameed
doaj   +1 more source

On a semilinear elliptic equation with inverse-square potential [PDF]

Selecta Mathematica, 2005
We study the existence and nonexistence of solutions to a semilinear elliptic equation with inverse-square potential. The dividing line with respect to existence or nonexistence is given by a critical exponent, which depends on the strength of the potential.
Alberto Tesei, Louis Dupaigne, Haim Brezis, Haim Brezis   +3 more
openaire   +4 more sources

Convexity of solutions of semilinear elliptic equations

Duke Mathematical Journal, 1985
Theorem 1. Let \(\Omega\) be a domain in \({\mathbb{R}}^ 2,G,H\in C^{2+\alpha}\), \(\Delta w=G\cdot w+H\cdot w| \nabla w|^ 2>0\) in \(\Omega\), \[ (GG''-2G'{}^ 2)\cdot w+(GH''+G''H-4G'H')\cdot w| \nabla w|^ 2+(HH''-2H'{}^ 2)\cdot w| \nabla w|^ 4\leq 0 \] in \(\Omega\). If \(\phi (w)=2(\partial^ 2_ 1w\partial^ 2_ 2w- (\partial_ 1\partial_ 2w)^ 2)\geq 0\)
Caffarelli, Luis A., Friedman, Avner
openaire   +3 more sources

Existence of positive solutions for generalized quasilinear Schrödinger equations with Sobolev critical growth

Electronic Journal of Qualitative Theory of Differential Equations
In this paper, we are devoted to establishing that the existence of positive solutions for a class of generalized quasilinear elliptic equations in $\mathbb{R}^{N}$ with Sobolev critical growth, which have appeared from plasma physics, as well as high ...
Nian Zhang, Chuchu Liang
doaj   +1 more source

Multiple solutions of nonlinear partial functional differential equations and systems

Electronic Journal of Qualitative Theory of Differential Equations, 2019
We shall consider weak solutions of initial-boundary value problems for semilinear and nonlinear parabolic differential equations with certain nonlocal terms, further, systems of elliptic functional differential equations.
László Simon
doaj   +1 more source

On a semilinear elliptic equation in Hn

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2009
We prove existence/nonexistence and uniqueness of positive entire solutions for some semilinear elliptic equations on the Hyperbolic space.
Gianni Mancini, K. Sandeep
openaire   +3 more sources

Parallelization of Faber Polynomial Based Propagators for Laser Applications

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Volume 38, Issue 4, July/August 2025.
ABSTRACT In order to simulate a laser system, the evaluation of a complex semilinear master equation is needed, including the description of the wave propagation by Maxwell's equations and appropriate rate equations. The denser the spatial discretization, the slower the computation time of the time‐dependent propagator.
Wladimir Plotnikov, Dirk Schulz
wiley   +1 more source

Conformal metrics of constant scalar curvature with unbounded volumes

Proceedings of the London Mathematical Society, Volume 131, Issue 1, July 2025.
Abstract For n⩾25$n\geqslant 25$, we construct a smooth metric g∼$\tilde{g}$ on the standard n$n$‐dimensional sphere Sn$\mathbb {S}^n$ such that there exists a sequence of smooth metrics {g∼k}k∈N$\lbrace \tilde{g}_k\rbrace _{k\in \mathbb {N}}$ conformal to g∼$\tilde{g}$ where each g∼k$\tilde{g}_k$ has scalar curvature Rg∼k≡1$R_{\tilde{g}_k}\equiv 1 ...
Liuwei Gong, Yanyan Li
wiley   +1 more source

Second-Order Necessary Conditions for Optimal Control of Semilinear Elliptic Equations with Leading Term Containing Controls [PDF]

, 2017
An optimal control problem for a semilinear elliptic equation of divergence form is considered. Both the leading term and the semilinear term of the state equation contain the control.
H. Lou, J. Yong
semanticscholar   +1 more source

Forward uncertainty quantification in random differential equation systems with delta‐impulsive terms: Theoretical study and applications

Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7609-7629, 15 May 2025.
This contribution aims at studying a general class of random differential equations with Dirac‐delta impulse terms at a finite number of time instants. Our approach directly addresses calculating the so‐called first probability density function, from which all the relevant statistical information about the solution, a stochastic process, can be ...
Vicente J. Bevia, Juan C. Cortés, Rafael J. Villanueva   +2 more
wiley   +1 more source