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Dynamics of soliton propagation: bifurcation, chaos, and quantitative insights into the modified Camassa-Holm equation. [PDF]

Sci Rep
Alam MN, Ahmed SF, Ismael HF, Firdi MD, Badruddin IA, Javed S.   +5 more
europepmc   +1 more source

A multiscale theory for network advection- reaction-diffusion. [PDF]

J Math Biol
Oliveri H, Cozzolino E, Goriely A.
europepmc   +1 more source

‘reportless places’: Janet Malcolm and Collage

Critical Quarterly, EarlyView.
Natalie Ferris
wiley   +1 more source

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On Weak Solutions of Elliptic Equations with Singular Drifts

SIAM Journal on Mathematical Analysis, 2015
Summary: We consider the Dirichlet problem for second-order linear elliptic equations with singular drift terms given by a vector field \(u\). \(W^{1,p}\)-estimates for weak solutions are quite well known, provided that \(u\) is sufficiently regular, e.g., \(u \in L^\infty\).
Hyunseok Kim, Young-Heon Kim
exaly   +3 more sources

Nonlinear elliptic equations with singular nonlinearities

Asymptotic Analysis, 2013
In this paper we study nonlinear elliptic boundary value problems with singular nonlinearities whose simplest example is −div (|∇u|p−2∇u)=f/uγ in Ω, u=0 on ∂Ω, where Ω is a bounded open set in RN (N≥2), γ>0 ...
DE CAVE, LINDA MARIA
openaire   +3 more sources

Lyapunov‐type inequalities for singular elliptic partial differential equations

Mathematical Methods in the Applied Sciences, 2021
We establish Lyapunov-type inequalities for a class of singular elliptic partial differential equations. As an application of Lyapunov-type inequalities, we obtain lower bounds for the first eigenvalue of the associated singular elliptic partial ...
Dharmendra Kumar, Jagmohan Tyagi
exaly   +2 more sources

Semilinear Elliptic Equations with Singularity on the Boundary

Journal of Partial Differential Equations, 2002
This paper is devoted to the semilinear elliptic problem \[ \begin{cases} -\Delta u=K(x) \bigl(1-|x|\bigr)^{-\lambda} u^q,\quad & x\in B,\\ u(x)>0, \quad & x\in B,\\ u(x)=0, \quad & x\in\partial B,\end{cases} \tag{1} \] where \(\lambda >0\), \(q>1\) and \(K(x)\) is a given nonnegative \(\alpha\)-Hölder continuous function on \(\overline B\).
Zeng, Youdong, Chen, Zuchi
openaire   +2 more sources

Nonlinear Singular Elliptic Equations

Journal of the London Mathematical Society, 1989
Let F be a dense vector subspace of a Banach space E, and f be a functional defined on F, in which f is not expected to have any critical point. We extend the variational theory to seek generalized critical points of f in E (not in F). Using these results we find solutions in \(W_ 0^{1,2}(\Omega)\) of the following equation \[ (P)\quad -\Delta u+c=Ke ...
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An elliptic equation with singular nonlinearity

Communications in Partial Differential Equations, 1987
The purpose of this paper is to study the problem (P) −Δu+u−α=f in Ω, u=0 on ∂Ω, u−α∈L1(Ω), u>0 in Ω, where Ω is a bounded smooth open set of RN, f≥0, f∈L1(Ω) and ...
J. I. Diaz, J.M. Morel, L. Oswald
openaire   +1 more source

Nonlinear Elliptic Equations with Mixed Singularities

Potential Analysis, 2017
This paper deals with the mathematical analysis of a class of non-variational degenerate elliptic equations with mixed singular structures. A feature of the paper under review is that the singular structure arises both at the set of critical points and on the ground touching points. The main result of this paper establishes that positive solutions have
openaire   +3 more sources