Results 41 to 50 of about 232 (187)

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 ...
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Six One‐Sign Solutions for Semilinear Elliptic Problems in ℝN*

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
In this work, we consider the existence of one‐sign solutions for semilinear elliptic problems: {−Δu = λa(x)f(u), in ℝN, u(x)⟶0, as|x|⟶+∞, where N ≥ 3, λ is a real parameter and a ∈ C(ℝN, ℝ) is a weighted function, f ∈ C(ℝ, ℝ). Furthermore, by bifurcation technique, we identify the interval of bifurcation parameter in which the semilinear elliptic ...
Wenguo Shen, Claudia Capone
wiley   +1 more source

Asymptotic behavior and uniqueness of boundary blow-up solutions to elliptic equations

Electronic Journal of Qualitative Theory of Differential Equations, 2015
In this paper, under some structural assumptions of weight function $b(x)$ and nonlinear term $f(u)$, we establish the asymptotic behavior and uniqueness of boundary blow-up solutions to semilinear elliptic equations \begin{equation*} \begin{cases ...
Qiaoyu Tian, Yonglin Xu
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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
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On the principle of linearized stability for quasilinear evolution equations in time‐weighted spaces

Mathematische Nachrichten, Volume 298, Issue 12, Page 3939-3959, December 2025.
Abstract Quasilinear (and semilinear) parabolic problems of the form v′=A(v)v+f(v)$v^{\prime }=A(v)v+f(v)$ with strict inclusion dom(f)⊊dom(A)$\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ of the domains of the function v↦f(v)$v\mapsto f(v)$ and the quasilinear part v↦A(v)$v\mapsto A(v)$ are considered in the framework of time‐weighted function spaces ...
Bogdan‐Vasile Matioc, Lina Sophie Schmitz, Christoph Walker   +2 more
wiley   +1 more source

A Singular Semilinear Elliptic Equation with a Variable Exponent

Advanced Nonlinear Studies, 2016
Abstract In this paper we consider singular semilinear elliptic equations with a variable exponent whose model problem is
Carmona Tapia, José, Martínez Aparicio, Pedro Jesús   +1 more
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Weak solutions for a singular beam equation

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 105, Issue 12, December 2025.
Abstract This paper deals with a dynamic Gao beam of infinite length subjected to a moving concentrated Dirac mass. Under appropriate regularity assumptions on the initial data, the problem possesses a weak solution which is obtained as the limit of a sequence of solutions of regularized problems.
Olena Atlasiuk, Arnaud Heibig, Adrien Petrov   +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  

Quasilinear Degenerate Evolution Systems Modelling Biofilm Growth: Well‐Posedness and Qualitative Properties

Mathematical Methods in the Applied Sciences, Volume 48, Issue 16, Page 14890-14908, 15 November 2025.
ABSTRACT We analyze nonlinear degenerate coupled partial differential equation (PDE)‐PDE and PDE‐ordinary differential equation (ODE) systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular diffusion.
K. Mitra, S. Sonner
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
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