Multiple of Homoclinic Solutions for a Perturbed Dynamical Systems with Combined Nonlinearities
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DOI: 10.1007/s00009-017-0930-x
Abstract: In this paper, we study the existence of multiple and infinite homoclinic solutions for the following perturbed dynamical systems $$\begin{aligned} \ddot{x}+A\cdot \dot{x}-L(t)\cdot x+\nabla W(t,x)=f(t), \end{aligned}$$x¨+A·x˙-L(t)·x+∇W(t,x)=f(t),where $$t\in {\mathbb R}, x\in {\mathbb R}^N,$$t∈R,x∈RN,A is an antisymmetric constant… read more here.
Keywords: homoclinic solutions; multiple homoclinic; mathbb mathbb; dynamical systems ... See more keywords
Codiagonalization of Matrices and Existence of Multiple Homoclinic Solutions
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DOI: 10.11948/2017012
Abstract: The purpose of this paper is twofold. First, we use Lagrange’s method and the generalized eigenvalue problem to study systems of two quadratic equations. We find exact conditions so the system can be codiagonalized and… read more here.
Keywords: codiagonalization; codiagonalization matrices; homoclinic solutions; multiple homoclinic ... See more keywords