LAUSR

Multiple of Homoclinic Solutions for a Perturbed Dynamical Systems with Combined Nonlinearities

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0 Published in 2017 at "Mediterranean Journal of Mathematics"

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

Heteroclinic and homoclinic solutions for nonlinear second-order coupled systems with $$\phi $$-Laplacians

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0 Published in 2021 at "Computational and Applied Mathematics"

DOI: 10.1007/s40314-021-01556-w

Abstract: In this paper we present sufficient conditions for the existence of heteroclinic or homoclinic solutions for second order coupled systems of differential equations on the real line. We point out that it is required only… read more here.

Keywords: order coupled; heteroclinic homoclinic; second order; homoclinic solutions ... See more keywords

Existence of homoclinic solutions for nonlinear second-order coupled systems

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0 Published in 2019 at "Journal of Differential Equations"

DOI: 10.1016/j.jde.2018.07.072

Abstract: Abstract This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature. The arguments… read more here.

Keywords: order coupled; existence homoclinic; homoclinic solutions; solutions nonlinear ... See more keywords

A note on homoclinic solutions of (p,q)-Laplacian difference equations

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1 Published in 2019 at "Journal of Difference Equations and Applications"

DOI: 10.1080/10236198.2019.1572128

Abstract: We prove the existence of at least two positive homoclinic solutions for a discrete boundary value problem of equations driven by the -Laplace operator. The properties of the nonlinearity ensure that the energy functional, corresponding… read more here.

Keywords: difference equations; laplacian difference; note homoclinic; solutions laplacian ... See more keywords

Homoclinic solutions for Hamiltonian systems with variable-order fractional derivatives

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0 Published in 2019 at "Complex Variables and Elliptic Equations"

DOI: 10.1080/17476933.2019.1652281

Abstract: ABSTRACT In this paper, we are concerned with the multiplicity and concentration of solutions for a Hamiltonian system driven by the fractional Laplace operator with variable order derivative. More precisely, we consider where , ,… read more here.

Keywords: order; homoclinic solutions; systems variable; hamiltonian systems ... See more keywords

Homoclinic Solutions for a Higher Orderϕc-Laplacian Difference Equation Containing Both Advance and Retardation

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0 Published in 2019 at "Mathematical Problems in Engineering"

DOI: 10.1155/2019/3624842

Abstract: We consider a 2mth-order nonlinear difference equation containing both advance and retardation withϕc-Laplacian. Using the critical point theory, some new and concrete criteria for the existence of homoclinic solutions with mixed nonlinearities are obtained. read more here.

Keywords: equation containing; order; homoclinic solutions; containing advance ... See more keywords

Codiagonalization of Matrices and Existence of Multiple Homoclinic Solutions

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0 Published in 2017 at "Journal of Applied Analysis and Computation"

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

Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential

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0 Published in 2017 at "Mathematica Slovaca"

DOI: 10.1515/ms-2016-0285

Abstract: Abstract A result for the existence of homoclinic orbits is obtained for (q, p)-Laplacian systems. read more here.

Keywords: systems coercive; homoclinic solutions; ordinary laplacian; coercive potential ... See more keywords

Some multiplicity results of homoclinic solutions for second order Hamiltonian systems

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0 Published in 2020 at "Opuscula Mathematica"

DOI: 10.7494/opmath.2020.40.1.21

Abstract: where q : R → R , W ∈ C1(R × R ,R) and ∇W (t, q) denotes the gradient of W with respect to q ∈ R for every t ∈ R. We look… read more here.

Keywords: solutions second; results homoclinic; second order; homoclinic solutions ... See more keywords