Existence of homoclinic solutions for a class of second-order non-autonomous Hamiltonian systems

Abstract

ABSTRACT. By using the variant version of Mountain Pass Theorem, the existence of homoclinic solutions for a class of second-order Hamiltonian systems is obtained. The result obtained generalizes and improves some known works.

Existence and Multiplicity of Fast Homoclinic Solutions for a Class of Nonlinear Second-Order Nonautonomous Systems in a Weighted Sobolev Space

“…Remark 6. We point out that (K1) is used in [13]. There are functions which can not be written in the form (1/2)( ( ) , ); then the results we obtain here are different.…”

“…In the past years, many researchers paid attention to the existence and multiplicity of homoclinic solutions for systems (3) and (5) by critical point theory. For example, see [2][3][4][5][6][7][8][9][10][11][12][13] and references cited therein. However, there is only a few researches about the existence of homoclinic solutions for damped vibration problems (4) when ( ) ̸ = 0.…”

New homoclinic solutions for a class of second-order Hamiltonian systems with a mixed condition

“…In the last two decades, many mathematicians have successfully used variational methods to obtain the existence and multiplicity of homoclinic orbits for problem (1) such as [1,[3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Since this problem is considered in the whole space, one of the main difficulties is the lack of compactness of embedding.…”

Existence of fast homoclinic solutions for a class of second-order damped vibration systems

“…For example, see [8][9][10][11][12][13][14][15][16][17][18][19], and the references cited therein. For the existence of homoclinic solutions for damped vibration problem (1.4), please see the literature [20][21][22][23][24][25], and the references cited therein.…”