Results 101 to 110 of about 9,595 (205)
Journal of Applied Mathematics, 2012 The authors study the existence and uniqueness of a set with 2kT-periodic solutions for a class of second-order differential equations by using Mawhin's continuation theorem and some analysis methods, and then a unique homoclinic orbit is obtained as a ...
Lijuan Chen, Shiping Lu
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Homoclinic solutions for second order Hamiltonian systems with general potentials near the origin
Electronic Journal of Qualitative Theory of Differential Equations, 2013 In this paper, we study the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems with general potentials near the origin. Recent results from the literature are generalized and significantly improved.
Qingye Zhang
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Abstract and Applied Analysis, 2014 We investigate a class of nonperiodic fourth order differential equations with general potentials. By using variational methods and genus properties in critical point theory, we obtain that such equations possess infinitely homoclinic solutions.
Liu Yang
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Multiple homoclinic solutions for a class of nonhomogeneous Hamiltonian systems
Boundary Value Problems, 2018 By introducing a new superquadratic condition, we obtain the existence of two nontrivial homoclinic solutions for a class of perturbed second order Hamiltonian systems which are obtained by the mountain pass theorem and Ekeland’s variational principle.
Chunhua Deng, Dong-Lun Wu
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Electronic Journal of Qualitative Theory of Differential Equations, 2019 This paper is concerned with the existence of positive even homoclinic solutions for the $p$-Laplacian equation \begin{equation*} (|u'|^{p-2}u')' - a(t)|u|^{p-2}u+f(t,u)=0,\qquad t\in \mathbb{R}, \end{equation*} where $p\ge 2$ and the functions $a ...
Adel Daouas, Monia Boujlida
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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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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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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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