Results 51 to 60 of about 376,175 (295)

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

Symmetry breaking and semilinear elliptic equations

Journal of Computational and Applied Mathematics, 1989
It is a readily observable fact that many physical and mathematical systems possess a degree of symmetry and that a study of this symmetry may give us valuable insight into their behaviour. It is particularly interesting that symmetric systems exist which possess non-symmetric solutions and where this solution branch arises from a symmetry breaking ...
openaire   +2 more sources

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

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

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

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

Renormalized solutions of semilinear elliptic equations with general measure data [PDF]

Monatshefte für Mathematik (Print), 2016
In the paper we first propose a definition of renormalized solution of semilinear elliptic equation involving operator corresponding to a general (possibly nonlocal) symmetric regular Dirichlet form satisfying the so-called absolute continuity condition ...
Tomasz Klimsiak, A. Rozkosz
semanticscholar   +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

Rectifiability, finite Hausdorff measure, and compactness for non‐minimizing Bernoulli free boundaries

Communications on Pure and Applied Mathematics, Volume 78, Issue 3, Page 545-591, March 2025.
Abstract While there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less is known about critical points of the corresponding energy. Saddle points of the energy (or of closely related energies) and solutions of the corresponding time‐dependent ...
Dennis Kriventsov, Georg S. Weiss
wiley   +1 more source