Results 51 to 60 of about 151 (130)

Existence, uniqueness and multiplicity of positive solutions for some nonlocal singular elliptic problems

Electronic Journal of Differential Equations, 2017
In this article, using the sub-supersolution method and Rabinowitz-type global bifurcation theory, we prove some results on existence, uniqueness and multiplicity of positive solutions for some singular nonlocal elliptic problems.
Baoqiang Yan, Qianqian Ren
doaj  

Boundary spike‐layer solutions of the multi‐dimensional singular Keller–Segel system: Existence, profiles and stability

Proceedings of the London Mathematical Society, Volume 132, Issue 2, February 2026.
Abstract This paper investigates boundary‐layer solutions of the singular Keller–Segel system (proposed in Keller and Segel [J. Theor. Biol. 30 (1971), 377–380]) in multi‐dimensional domains, which describes cells' chemotactic movement toward the concentration gradient of the nutrient they consume, subject to a zero‐flux boundary condition for the cell
Jose A. Carrillo, Jingyu Li, Zhi‐An Wang, Wen Yang   +3 more
wiley   +1 more source

Viscosity Solutions for First‐Order PDEs With Measurable Coefficients and Superlinear Gradient Growth

Journal of Mathematics, Volume 2026, Issue 1, 2026.
Inspired by a fundamental existence result in the theory of PDEs, we present a general existence theorem for viscosity solutions in the standard sense that is applicable to a wide class of partial differential equations. These equations are characterized by coefficients that are merely measurable, with no continuity assumptions imposed.
S. M. E. Hosseini, S. S. Nezhad, Dimitri Mugnai   +2 more
wiley   +1 more source

Existence and comparison results for quasilinear evolution hemivariational inequalities

Electronic Journal of Differential Equations, 2004
We generalize the sub-supersolution method known for weak solutions of single and multivalued nonlinear parabolic problems to quasilinear evolution hemivariational inequalities.
Siegfried Carl, Vy K. Le, Dumitru Motreanu   +2 more
doaj  

Positive solutions for Sturm-Liouville BVPs on time scales via sub-supersolution and variational methods [PDF]

Boundary Value Problems, 2013
Abstract This paper is concerned with the existence of one and two positive solutions for the following Sturm-Liouville boundary value problem on time scales { −
Zhang, Quan-Guo, He, Xi-Ping, Sun, Hong-Rui   +2 more
openaire   +1 more source

On classification of global dynamics for energy‐critical equivariant harmonic map heat flows and radial nonlinear heat equation

Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1783-1842, September 2025.
Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
wiley   +1 more source

Existence of positive solutions for fractional Laplacian equations: theory and numerical experiments

Electronic Journal of Differential Equations, 2020
We consider a class of nonlinear fractional Laplacian problems satisfying the homogeneous Dirichlet condition on the exterior of a bounded domain. We prove the existence of positive weak solution for classes of sublinear nonlinearities including ...
Maya Chhetri, Petr Girg, Elliott Hollifield   +2 more
doaj  

The existence of positive solution for singular Kirchhoff equation with two parameters

Boundary Value Problems, 2019
In this paper, we consider the singular Kirchhoff equation with two parameters {−a(∫Ω|∇u(x)|2dx)△u(x)+K(x)g(u)=λf(x,u)+μh(x)in Ω,u>0in Ω,u=0on ∂Ω. $$\textstyle\begin{cases} -a ( \int_{\varOmega}|\nabla u(x)|^{2}\,dx )\triangle u(x)+K(x)g(u)=\lambda f(x,u)
Ke Di, Baoqiang Yan
doaj   +1 more source

The robust Orlicz risk with an application to the green photovoltaic power generation

Asian Journal of Control, Volume 27, Issue 4, Page 1655-1667, July 2025.
Abstract We propose a novel recursive utility for controlling stochastic processes under risk and uncertainty. Our formulation uses a robustified Orlicz risk that can evaluate risk and uncertainty simultaneously. We focus on the control problem of a photovoltaic power generation system that supplies excess electricity for the secondary purpose of ...
Hidekazu Yoshioka, Motoh Tsujimura
wiley   +1 more source

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