Results 41 to 50 of about 145 (131)

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

Discontinuous Variational-Hemivariational Inequalities Involving the -Laplacian

Journal of Inequalities and Applications, 2007
We deal with discontinuous quasilinear elliptic variational-hemivariational inequalities. By using the method of sub- and supersolutions and based on the results of S. Carl, we extend the theory for discontinuous problems.
Winkert Patrick
doaj  

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

Positive solutions of higher order quasilinear elliptic equations

Abstract and Applied Analysis, 2002
The higher order quasilinear elliptic equation −Δ(Δp(Δu))=f(x,u) subject to Dirichlet boundary conditions may have unique and regular positive solution. If the domain is a ball, we obtain a priori estimate to the radial solutions via blowup.
Marcelo Montenegro
doaj   +1 more source

Corrigendum to Multiplicity of positive weak solutions to subcritical singular elliptic Dirichlet problems

Electronic Journal of Qualitative Theory of Differential Equations, 2018
This paper serves as a corrigendum to the paper "Multiplicity of positive weak solutions to subcritical singular elliptic Dirichlet problems", published in Electron J. Qual. Theory Differ. Equ. 2017, No. 100, 1–30.
Tomas Godoy, Alfredo Guerin
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

Nonuniqueness of solutions of initial-value problems for parabolic p-Laplacian

Electronic Journal of Differential Equations, 2015
We construct a positive solution to a quasilinear parabolic problem in a bounded spatial domain with the p-Laplacian and a nonsmooth reaction function. We obtain nonuniqueness for zero initial data.
Jiri Benedikt, Vladimir E. Bobkov, Petr Girg, Lukas Kotrla, Peter Takac   +4 more
doaj  

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

Existence of solutions for a nonlinear degenerate elliptic system

Electronic Journal of Differential Equations, 2004
In this paper, we study the existence of solutions for degenerate elliptic systems. We use the sub-super solution method, and the existence of classical and weak solutions.
Nguyen Minh, Tran Dinh Ke
doaj