Results 51 to 60 of about 1,359 (222)

Homoclinic Solutions of an Integral Equation: Existence and Stability

Journal of Differential Equations, 1999
The authors study (stationary) evolution equation in the form of the following nonlinear convolution type integral equation \[ (J\ast u)(x)- u(x)-f[u(x)]=0,\tag{1} \] with the condition \(u(\pm \infty)=0.\) It is assumed, that \(J(z)\geq 0\), \(\int J(z) dz =1\) and \(f\) is bistable. They construct homoclinic (even) solutions to the equation (1).
Chmaj, Adam, Ren, Xiaofeng
openaire   +2 more sources

Homoclinic solutions for Hamiltonian system with impulsive effects

Advances in Difference Equations, 2018
In this article, we investigate a class of impulsive Hamiltonian systems with a p-Laplacian operator. By establishing a series of new sufficient conditions, the existence of homoclinic solutions to such type of systems is revealed.
Jian Liu, Lizhao Yan, Fei Xu, Mingyong Lai   +3 more
doaj   +1 more source

Multiple Periodic solutions and Positive Homoclinic Solution for a differential equation

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2013
The authors consider the nonautonomous differential equation \[ x''-a(t)x+b(t)x^2+c(t)x^3=0, \] where \(a,b\) and \(c\) are continuous \(T\)-periodic functions and obtain two results for them. The first one gives, under certain additional hypotheses, the existence of at least two nontrivial \(T\)-periodic solutions.
de Araujo, Anderson L. A., Pedroso, Kennedy Martins   +1 more
openaire   +3 more sources

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9814-9831, June 2026.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +1 more source

Global bifurcation of homoclinic solutions of Hamiltonian systems

Discrete and Continuous Dynamical Systems, 2003
We provide global bifurcation results for a class of nonlinear hamiltonian ...
Secchi, S, Stuart, CA
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

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

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

Periodic and Homoclinic Solutions of Extended Fisher–Kolmogorov Equations

Journal of Mathematical Analysis and Applications, 2000
The authors study the existence of periodic and homoclinic solutions to fourth-order semilinear equations via variational methods.
Tersian, Stepan, Chaparova, Julia
openaire   +2 more sources

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