Results 81 to 90 of about 697 (183)
Multiple homoclinic solutions for singular differential equations
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2010 The homoclinic bifurcations of ordinary differential equation under singular perturbations are considered. We use exponential dichotomy, Fredholm alternative and scales of Banach spaces to obtain various bifurcation manifolds with finite codimension in an appropriate infinite-dimensional space. When the perturbative term is taken from these bifurcation
Zhu, Changrong +2 more
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Homoclinic solutions of singular differential equations with $\phi$-Laplacian
Electronic Journal of Qualitative Theory of Differential Equations, 2018 Summary: A singular nonlinear initial value problem (IVP) with a \(\phi\)-Laplacian of the form \[ (p(t)\phi(u'(t)))'+ p(t)f(\phi(u(t)))=0, \quad u(0)=u_0 \in [L_0,L),\quad u'(0)=0 \] is investigated on the half-line \([0,\infty)\). Here, \(\phi\) is smooth and increasing on \(\mathbb{R}\) with \(\phi(0)=0\), \(f\) is locally Lipschitz continuous with ...
Lukas, Rachunek, Irena, Rachunkova
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HOMOCLINIC SOLUTIONS OF DISCRETE NONLINEAR SYSTEMS VIA VARIATIONAL METHOD
Journal of Applied Analysis & Computation, 2019 Summary: Homoclinic solutions arise in various discrete models with variational structure, from discrete nonlinear Schrödinger equations to discrete Hamiltonian systems. In recent years, a lot of interesting results on the homoclinic solutions of difference equations have been obtained.
Erbe, Lynn, Jia, Baoguo, Zhang, Qinqin
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Advances in Difference Equations, 2018 In this paper, we investigate the existence of a set with 2kT $2kT$-periodic solutions for n-dimensional p-Laplacian neutral differential systems with a time-varying delay (φp(u(t)−Cu(t−τ))′)′+ddt∇F(u(t))+G(u(t−γ(t)))=ek(t) $(\varphi_{p}(u(t)-Cu(t-\tau ))
Fang Gao, Wenbin Chen
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Electronic Journal of Differential Equations, 2015 In this article, we sutdy the multiplicity of homoclinic solutions to the perturbed second-order discrete Hamiltonian system $$ \Delta[p(n)\Delta u(n-1)]-L(n)u(n)+\nabla W(n,u(n))+\theta\nabla F(n,u(n))=0, $$ where L(n) and W(n,x) are neither ...
Liang Zhang, Xianhua Tang
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Partial Differential Equations in Applied MathematicsIn this work, we develop multi-wave, homoclinic breathers, M-shaped rational, 1-kink interactions with M-shaped, periodic-cross rational and kink-cross rational solutions for the fifth-order Sawada-Kotera equation, which represents the motion of long ...
Sajawal Abbas Baloch +4 more
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Normalized homoclinic solutions of discrete nonlocal double phase problems
Bulletin of Mathematical SciencesThe aim of this paper is to discuss the existence of normalized solutions to the following nonlocal double phase problems driving by the discrete fractional Laplacian: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] if [Formula: see text], [Formula: see text] if [Formula:
Mingqi Xiang, Yunfeng Ma, Miaomiao Yang
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Multibump solutions for an almost periodically forced singular Hamiltonian system
Electronic Journal of Differential Equations, 1995 existence of so-called multibump homoclinic solutions for a family of singular Hamiltonian systems in $R^2$ which are subjected to almost periodic forcing in time.
Paul H. Rabinowitz
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Existence of homoclinic solutions for Hamiltonian systems
Advances in Differential Equations, 2002 Using variational methods, the existence of homoclinic solutions is shown for the Hamiltonian system \(Ju'(x)+Mu(x)-\nabla_uF(x,u(x))=\lambda u(x)\), where \(u : \mathbb{R}\to \mathbb{R}^{2N}\), \(J\), \(M\) are matrices such that \(J=-J^T=-J^{-1}\), \(M^T=M\) and \(F\) is a Carathéodory nonlinearity satisfying addition properties.
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Homoclinic orbit solutions of a one Dimensional Wilson-Cowan type model
Electronic Journal of Differential Equations, 2008 We analyze a time independent integral equation defined on a spatially extended domain which arises in the modelling of neuronal networks. In this paper, the coupling function is oscillatory and the firing rate is a smooth "heaviside-like" function ...
Edward P. Krisner
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