Results 61 to 70 of about 15,562 (203)

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  

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

Renormalized solutions of semilinear equations involving measure data and operator corresponding to Dirichlet form

, 2015
We generalize the notion of renormalized solution to semilinear elliptic and parabolic equations involving operator associated with general (possibly nonlocal) regular Dirichlet form and smooth measure on the right-hand side.
Klimsiak, Tomasz, Rozkosz, Andrzej
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

Super and subsolutions for elliptic equations on all of ℝn

International Journal of Mathematics and Mathematical Sciences, 2002
By construction sub and supersolutions for the following semilinear elliptic equation −△u(x)=λg(x)f(u(x)), x∈ℝn which arises in population genetics, we derive some results about the theory of existence of solutions as well as asymptotic properties of the
G. A. Afrouzi, H. Ghasemzadeh
doaj   +1 more source

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

Uniqueness of positive solutions for cooperative Hamiltonian elliptic systems

Electronic Journal of Differential Equations, 2016
The uniqueness of positive solution of a semilinear cooperative Hamiltonian elliptic system with two equations is proved for the case of sublinear and superlinear nonlinearities. Implicit function theorem, bifurcation theory, and ordinary differential
Junping Shi, Ratnasingham Shivaji
doaj  

A nonlinear characterization of stochastic completeness of graphs

Mathematische Nachrichten, Volume 298, Issue 3, Page 925-943, March 2025.
Abstract We study nonlinear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semilinear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a nonlinear setting. We provide characterizations for this property in terms of a semilinear Liouville theorem.
Marcel Schmidt, Ian Zimmermann
wiley   +1 more source