Results 61 to 70 of about 1,967,647 (144)

Existence of viscosity solutions to abstract Cauchy problems via nonlinear semigroups

Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.
Abstract In this work, we provide conditions for nonlinear monotone semigroups on locally convex vector lattices to give rise to a generalized notion of viscosity solutions to a related nonlinear partial differential equation. The semigroup needs to satisfy a convexity estimate, so called K$K$‐convexity, with respect to another family of operators ...
Fabian Fuchs, Max Nendel
wiley   +1 more source

Limits of cubic differentials and buildings

Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.
Abstract In the Labourie–Loftin parameterization of the Hitchin component of surface group representations into SL(3,R)$\mathrm{SL}(3,\mathbb {R})$, we prove an asymptotic formula for holonomy along rays in terms of local invariants of the holomorphic differential defining that ray.
John Loftin, Andrea Tamburelli, Michael Wolf   +2 more
wiley   +1 more source

Existence and Nonexistence Results for Classes of Singular Elliptic Problem

Abstract and Applied Analysis, 2010
The singular semilinear elliptic problem -Δu+k(x)u-γ=λup in Ω, u>0 in Ω, u=0 on ∂Ω, is considered, where Ω is a bounded domain with smooth boundary in RN, k∈Clocα(Ω)∩C(Ω¯), and γ,p,λ are three positive constants.
Peng Zhang, Jia-Feng Liao
doaj   +1 more source

Asymptotic behavior of positive large solutions of semilinear Dirichlet problems

Electronic Journal of Qualitative Theory of Differential Equations, 2013
Let $\Omega $ be a smooth bounded domain in $\mathbb{R}^{n},\ n\geq 2$. This paper deals with the existence and the asymptotic behavior of positive solutions of the following problems \begin{equation*} \Delta u=a(x)u^{\alpha },\alpha >1\text{ and }\Delta
Habib Maagli, Sonia Ben Othman, Rym Chemmam   +2 more
doaj   +1 more source

Regularity Properties of Solutions of a Model for Morphoelastic Growth in the Presence of Nutrients in One Spatial Dimension

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 1, March 2026.
ABSTRACT Regularity properties of solutions for a class of quasi‐stationary models in one spatial dimension for stress‐modulated growth in the presence of a nutrient field are proven. At a given point in time the configuration of a body after pure growth is determined by means of a family of ordinary differential equations in every point in space ...
Julian Blawid, Georg Dolzmann
wiley   +1 more source

Liouville properties for differential inequalities with (p,q)$(p,q)$ Laplacian operator

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract In this paper, we establish several Liouville‐type theorems for a class of nonhomogenenous quasilinear inequalities. In the first part, we prove various Liouville results associated with nonnegative solutions to Ps$P_s$ −Δpu−Δqu⩾us−1inΩ,$$\begin{equation} -\Delta _p u-\Delta _q u\geqslant u^{s-1} \, \text{ in }\, \Omega, \end{equation}$$where ...
Mousomi Bhakta, Anup Biswas, Roberta Filippucci   +2 more
wiley   +1 more source

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

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

Fractional double-phase nonlocal equation in Musielak-Orlicz Sobolev space

Boundary Value Problems
In this paper, we analyze the existence of solutions to a double-phase fractional equation of the Kirchhoff type in Musielak-Orlicz Sobolev space with variable exponents.
Tahar Bouali, Rafik Guefaifia, Salah Boulaaras   +2 more
doaj   +1 more source