Results 1 to 10 of about 7,158,567 (167)
Multiple homoclinic solutions for a class of nonhomogeneous Hamiltonian systems [PDF]
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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Multiple homoclinic solutions for superquadratic Hamiltonian systems [PDF]
Electronic Journal of Differential Equations, 2016 In this article we study the existence of infinitely many homoclinic solutions for a class of second-order Hamiltonian systems $$ \ddot{u}-L(t)u+W_u(t,u)=0, \quad \forall t\in\mathbb{R}, $$ where L is not required to be either uniformly positive ...
Wei Jiang, Qingye Zhang
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Multiple homoclinic solutions for a one-dimensional Schrödinger equation [PDF]
Discrete and Continuous Dynamical Systems - Series S, 2016 This paper is dedicated to the study of the problem of existence of homoclinic solutions to a Schrödinger equation of the form \[ x''-V(t)x+x^3=0,\eqno{(1)} \] where \(V:\mathbb R\to\mathbb R\) is a \(L^1\)-function.
Duccio Papini
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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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Multiple homoclinic solutions for p-Laplacian Hamiltonian systems with concave–convex nonlinearities [PDF]
Boundary Value Problems, 2020 The multiplicity of homoclinic solutions is obtained for a class of the p-Laplacian Hamiltonian systems d d t ( | u ˙ ( t ) | p − 2 u ˙ ( t ) ) − a ( t ) | u ( t ) | p − 2 u ( t ) + ∇ W ( t , u ( t ) ) = 0 $\frac{d}{dt}(|\dot{u}(t)|^{p-2}\dot{u}(t))-a(t)|
Lili Wan
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Multiple transverse homoclinic solutions near a degenerate homoclinic orbit
Journal of Differential Equations, 2015 The authors study periodic perturbations of differential equations possessing a degenerate homoclinic orbit. Regarding the degeneracy it is assumed more precisely that along the homoclinic orbit the tangent spaces of the corresponding stable and unstable manifolds intersect in a two-dimensional space.
Xiao-Biao Lin, Changrong Zhu
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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. +1 more
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Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we obtain the multiplicity of homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign potentials. The concentration-compactness principle is applied to show the compactness. As a byproduct, we
Dong-Lun Wu
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Existence and multiplicity of homoclinic solutions for a difference equation
Electronic Journal of Differential Equations, 2020 The aim of this article is to obtain homoclinic solutions for a discrete problem involving p-Laplacian. We prove the existence of at least one, two and three solutions for the problem. Our approach is based on variational methods.
SHAPOUR HEIDARKHANI +2 more
openaire +4 more sources
Global Dynamic Analysis of a Typical Bistable Piezoelectric Cantilever Energy Harvesting System
Fractal and Fractional, 2023 This paper focuses on global dynamic behaviors of a bistable piezoelectric cantilever energy harvester with a tip magnet and a single external permanent magnet at the near side.
Diandian Cui, Huilin Shang
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