Results 71 to 80 of about 1,398 (233)

Separation Property of Solutions for a Semilinear Elliptic Equation [PDF]

Journal of Differential Equations, 2000
The authors consider the problem of finding a positive solution \(u\) of the differential equation \(\Delta u + K(|x|)u^p = 0\) in \(\mathbb{R}^n\setminus \{0\}\). Here \(K\) is a given function which is Hölder continuous in \(\mathbb{R}^n\setminus \{0\}\). Many authors (often in collaboration with Li) have studied this problem under various hypotheses
Liu, Yi, Li, Yi, Deng, Yinbin
openaire   +2 more sources

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 and multiplicity of solutions to semilinear elliptic equation with nonlinear term of superlinear and subcritical growth

Electronic Journal of Differential Equations, 2018
This article concerns the existence and multiplicity of solutions to the superlinear elliptic problems. We introduce a new superlinear condition which is proved to be weaker than the Ambrosetti-Rabinowitz condition, the nonquadratic condition, the ...
Xiao-Feng Ke, Chun-Lei Tang
doaj  

Some maximum principles in semilinear elliptic equations [PDF]

Proceedings of the American Mathematical Society, 1986
We develop maximum principles for functions defined on the solutions to a class of semilinear, second order, uniformly elliptic partial differential equations. These principles are related to recent theorems of Protter and Protter and Weinberger and to a technique initiated by Payne for the determination of gradient bounds on the solution of the ...
openaire   +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

Exact multiplicity of positive solutions to a superlinear problem

Electronic Journal of Differential Equations, 2003
We generalize previous uniqueness results on a semilinear elliptic equation with zero Dirichlet boundary condition and superlinear, subcritical nonlinearity.
Junping Shi
doaj  

Properties of the least action level and the existence of ground state solution to fractional elliptic equation with harmonic potential [PDF]

Opuscula Mathematica
In this article we consider the following fractional semilinear elliptic equation \[(-\Delta)^su+|x|^2u =\omega u+|u|^{2\sigma}u \quad \text{ in } \mathbb{R}^N,\] where \(s\in (0,1)\), \(N\gt 2s\), \(\sigma\in (0,\frac{2s}{N-2s})\) and \(\omega\in (0 ...
César E. Torres Ledesma, Hernán C. Gutierrez, Jesús A. Rodríguez, Manuel M. Bonilla   +3 more
doaj   +1 more source

LARGE SOLUTIONS FOR YAMABE AND SIMILAR PROBLEMS ON DOMAINS IN RIEMANNIAN MANIFOLDS

, 2011
We present a unified approach to study large positive solutions (i.e., u(x) -> infinity as x -> partial derivative Omega) of the equation Delta u + hu - k psi(u) = -f in an arbitrary domain Omega.
Martin Dindoš, Dindos, Martin; id_orcid
core   +1 more source

Oscillatory Radial Solutions of Semilinear Elliptic Equations

Journal of Mathematical Analysis and Applications, 1997
We study the oscillatory behavior of radial solutions of the nonlinear partial differential equation Δu + f(u) + g(|x|, u) = 0 inRn, where f and g are continuous restoring functions, uf(u) > 0 and ug(|x|, u) > 0 for u ≠ 0. We assume that for fixedq limu → 0(|f(u)|/|u|q) = B > 0, for 1 < q < n/(n − 2), and, additionally, that 2F(u) ≥ (1 − 2/n)uf(u) when
Derrick, William R., Chen, Shaohua, Cima, Joseph A.   +2 more
openaire   +2 more sources

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