Results 61 to 70 of about 3,396,163 (214)

Existence and multiplicity of homoclinic solutions for a second-order Hamiltonian system

Electronic Journal of Qualitative Theory of Differential Equations, 2019
In this paper, we find new conditions to ensure the existence of one nontrivial homoclinic solution and also infinitely many homoclinic solutions for the second order Hamiltonian system $$ \ddot{u}-a(t)|u|^{p-2}u+\nabla W(t,u)=0,\qquad t\in \mathbb{R}, $
Yiwei Ye
doaj   +1 more source

Infinite Homoclinic Solutions of the Discrete Partial Mean Curvature Problem with Unbounded Potential

Mathematics, 2022
The mean curvature problem is an important class of problems in mathematics and physics. We consider the existence of homoclinic solutions to a discrete partial mean curvature problem, which is tied to the existence of discrete solitons.
Yanshan Chen, Zhan Zhou
doaj   +1 more source

Global bifurcation of homoclinic solutions

Journal of Differential Equations
In the analysis of parametrized nonautonomous evolutionary equations, bounded entire solutions are natural candidates for bifurcating objects. Appropriate explicit and sufficient conditions for such branchings, however, require to combine contemporary functional analytical methods from the abstract bifurcation theory for Fredholm operators with tools ...
Iacopo P. Longo, Christian Pötzsche, Robert Skiba   +2 more
openaire   +2 more sources

Existence of Homoclinic Solutions for a Class of Nonlinear Difference Equations [PDF]

Advances in Difference Equations, 2010
The authors consider the nonlinear difference equation \[ \Delta(p(n)(\Delta u(n-1))^\delta)-q(n)(x(n))^\delta=f(n,u(n)),\quad n\in\mathbb{Z}, \] where \(\Delta\) is the usual forward difference operator, \(\delta\) is the ratio of odd positive integers, \(p,q\) are real sequences with \(p(n)\neq 0\), and \(f:\mathbb{Z}\times\mathbb{Z}\to\mathbb{R ...
Chen Peng, Tang XH
openaire   +4 more sources

Are physiological oscillations physiological?

The Journal of Physiology, Volume 604, Issue 9, Page 3672-3693, 1 May 2026.
Abstract figure legend Mechanisms and functions of physiological oscillations. Abstract Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function.
Lingyun (Ivy) Xiong, Alan Garfinkel
wiley   +1 more source

Homoclinic breather, periodic wave, lump solution, and M-shaped rational solutions for cold bosonic atoms in a zig-zag optical lattice

Nonlinear Engineering, 2023
In this article, the equation showing the cold bosonic atoms in a zig-zag optical lattice model for some breathers, M-shaped solution and lump soliton solution, homoclinic breather pulses, breather lump pulses, periodic-cross kink wave, kink cross ...
Rizvi Syed T. R., Seadawy Aly R., Ahmed Samia   +2 more
doaj   +1 more source

Existence and Spectral Stability Analysis of Viscous‐Dispersive Shock Profiles for Isentropic Compressible Fluids of Korteweg Type

Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.
ABSTRACT The system describing the dynamics of a compressible isentropic fluid exhibiting viscosity and internal capillarity in one space dimension and in Lagrangian coordinates, is considered. It is assumed that the viscosity and the capillarity coefficients are nonlinear smooth, positive functions of the specific volume, making the system the most ...
Raffaele Folino, Corrado Lattanzio, Ramón G. Plaza   +2 more
wiley   +1 more source

On the so called rogue waves in nonlinear Schrodinger equations

Electronic Journal of Differential Equations, 2016
The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schrodinger equation (NLS) provides a mechanism. A Peregrine wave solution can be obtained by taking the infinite spatial
Y. Charles Li
doaj  

Existence and Stability for Traveling Waves of Fourth‐Order Semilinear Wave and Schrödinger Equations

Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.
ABSTRACT We investigate the existence and spectral stability of traveling wave solutions for a class of fourth‐order semilinear wave equations, commonly referred to as beam equations. Using variational methods based on a constrained maximization problem, we establish the existence of smooth, exponentially decaying traveling wave profiles for wavespeeds
Vishnu Iyer, Ross Parker, Atanas G. Stefanov   +2 more
wiley   +1 more source

Robust homoclinic orbits in planar systems with Preisach hysteresis operator [PDF]

, 2016
We construct examples of robust homoclinic orbits for systems of ordinary differential equations coupled with the Preisach hysteresis operator. Existence of such orbits is demonstrated for the first time.
Pimenov, Alexander, Rachinskii, Dmitrii
core   +1 more source