Results 61 to 70 of about 394,604 (313)

The free boundary for semilinear problems with highly oscillating singular terms

Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.
Abstract We investigate general semilinear (obstacle‐like) problems of the form Δu=f(u)$\Delta u = f(u)$, where f(u)$f(u)$ has a singularity/jump at {u=0}$\lbrace u=0\rbrace$ giving rise to a free boundary. Unlike many works on such equations where f$f$ is approximately homogeneous near {u=0}$\lbrace u = 0\rbrace$, we work under assumptions allowing ...
Mark Allen, Dennis Kriventsov, Henrik Shahgholian   +2 more
wiley   +1 more source

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

Holomorphic extension of solutions of semilinear elliptic equations [PDF]

Nonlinear Analysis: Theory, Methods & Applications, 2011
We prove, for a wide class of semilinear elliptic differential and pseudodifferential equations in $\R^d$, that the solutions which are sufficiently regular and have a certain decay at infinity extend to holomorphic functions in sectors of $\mathbb{C}^d$, improving earlier results where the extension was shown for a strip.
CAPPIELLO, Marco, F. Nicola
openaire   +4 more sources

Arithmetic Satake compactifications and algebraic Drinfeld modular forms

Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.
Abstract In this article, we construct the arithmetic Satake compactification of the Drinfeld moduli schemes of arbitrary rank over the ring of integers of any global function field away from the level structure, and show that the universal family extends uniquely to a generalized Drinfeld module over the compactification.
Urs Hartl, Chia‐Fu Yu
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

On the behavior of solutions to Schr\"odinger equations with dipole-type potentials near the singularity

, 2007
Asymptotics of solutions to Schroedinger equations with singular dipole-type potentials is investigated. We evaluate the exact behavior near the singularity of solutions to elliptic equations with potentials which are purely angular multiples of radial ...
Felli, Veronica, Marchini, Elsa M., Terracini, Susanna   +2 more
core   +1 more source

A Non‐Intrusive, Online Reduced Order Method for Non‐Linear Micro‐Heterogeneous Materials

International Journal for Numerical Methods in Engineering, Volume 126, Issue 5, 15 March 2025.
ABSTRACT In this contribution we present an adaptive model order reduction technique for non‐linear finite element computations of micro‐heterogeneous materials. The presented projection‐based method performs updates of the reduced basis during the iterative process and at the end of each load step.
Yasemin von Hoegen, Rainer Niekamp, Jörg Schröder   +2 more
wiley   +1 more source

Pointwise decay and smoothness for semilinear elliptic equations and travelling waves

, 2015
We derive sharp decay estimates and prove holomorphic extensions for the solutions of a class of semilinear nonlocal elliptic equations with linear part given by a sum of Fourier multipliers with finitely smooth symbols at the origin.
Cappiello, Marco, Nicola, Fabio
core   +1 more source

Remarks on a semilinear elliptic equation on Rn

Journal of Differential Equations, 1988
On etudie l'equation elliptique semi-lineaire Δu−u+Q|u| P−1 u=0 dans R n , u≥0, u¬=0 dans R n et u→0 a l'infini avec p telle que ...
openaire   +3 more sources