Results 71 to 80 of about 651,324 (288)

Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.
ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
wiley   +1 more source

Existence and Multiplicity Results for Degenerate Elliptic Equations with Dependence on the Gradient

Boundary Value Problems, 2007
We study the existence of positive solutions for a class of degenerate nonlinear elliptic equations with gradient dependence. For this purpose, we combine a blowup argument, the strong maximum principle, and Liouville-type theorems to obtain a ...
Sebastian Lorca, Leonelo Iturriaga
doaj   +2 more sources

Classification of supersolutions and Liouville theorems for some nonlinear elliptic problems

, 2016
In this paper we consider positive supersolutions of the elliptic equation $-\triangle u = f(u) |\nabla u|^q$, posed in exterior domains of $\mathbb{R}^N$ ($N\ge 2$), where $f$ is continuous in $[0,+\infty)$ and positive in $(0,+\infty)$ and $q>0$.
M. Burgos-Pérez, J. García-Melián, A. Quaas   +2 more
semanticscholar   +1 more source

Liouville theorems for the polyharmonic Henon-Lane-Emden system [PDF]

, 2013
We study Liouville theorems for the following polyharmonic H\'{e}non-Lane-Emden system \begin{eqnarray*} \left\{\begin{array}{lcl} (-\Delta)^m u&=& |x|^{a}v^p \ \ \text{in}\ \ \mathbb{R}^n,\\ (-\Delta)^m v&=& |x|^{b}u^q \ \ \text{in}\ \ \mathbb{R}^n ...
Mostafa Fazly
semanticscholar   +1 more source

Spectral Parameter Power Series Representation for Regular Solutions of the Radial Dirac System

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT A spectral parameter power series (SPPS) representation for the regular solution of the radial Dirac system with complex coefficients is obtained, as well as a SPPS representation for the (entire) characteristic function of the corresponding spectral problem on a finite interval. Based on the SPPS representation, a numerical method for solving
Emmanuel Roque, Sergii M. Torba
wiley   +1 more source

On Hybrid Type Nonlinear Fractional Integrodifferential Equations

Mathematics, 2020
In this paper, we introduce and investigate a hybrid type of nonlinear Riemann Liouville fractional integro-differential equations. We develop and extend previous work on such non-fractional equations, using operator theoretical techniques, and find the ...
Faten H. Damag, Adem Kılıçman, Awsan T. Al-Arioi   +2 more
doaj   +1 more source

C∞$$ {C}^{\infty } $$‐Structures for Liénard Equations and New Exact Solutions to a Class of Klein–Gordon Equations

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Liénard equations are analyzed using the recent theory of 𝒞∞‐structures. For each Liénard equation, a 𝒞∞‐structure is determined by using a Lie point symmetry and a 𝒞∞‐symmetry. Based on this approach, a novel method for integrating these equations is proposed, which consists in solving sequentially two completely integrable Pfaffian equations.
Beltrán de la Flor, Adrián Ruiz, Concepción Muriel   +2 more
wiley   +1 more source

Aspects of (2+1) dimensional gravity: AdS3 asymptotic dynamics in the framework of Fefferman-Graham-Lee theorems [PDF]

, 1999
Using the Chern-Simon formulation of (2+1) gravity, we derive, for the general asymptotic metrics given by the Fefferman-Graham-Lee theorems, the emergence of the Liouville mode associated to the boundary degrees of freedom of (2+1) dimensional anti de ...
Rooman, M., Spindel, Ph.
core   +1 more source

On Holditch and Liouville theorems

Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 1995
The authors examine the relationship between the Liouville theorem in mechanics and the Holditch theorem in geometry. They first start by introducing well-known results of Hamiltonian mechanics when the Hamiltonian comes from a Riemannian metric \[ ds^2=g_{ij}dx^idx^j \] on the configuration space. In particular, the authors prove that the solutions of
Hacisalihoǧlu, H. H., Amirov, A. Kh.
openaire   +4 more sources

Temporal pulse shaping aspects of refractive X‐ray lenses

Journal of Synchrotron Radiation, EarlyView.
This work investigates the temporal effects of refractive X‐ray lenses on ultra‐short pulses from X‐ray free‐electron lasers. Using both a full Fresnel theory model and a simplified ray‐tracing approach, the paper analyzes the pulse elongation and spatio‐temporal distortions introduced by these focusing optics.Refractive X‐ray lenses are frequently ...
Fabian Trost, Johan Bielecki, Richard Bean   +2 more
wiley   +1 more source