Infinitely many homoclinic solutions for a class of damped vibration problems
In this paper, we consider the multiplicity of homoclinic solutions for the following damped vibration problems x¨(t) + Bx˙(t) − A(t)x(t) + Hx(t, x(t)) = 0, where A(t) ∈ (R, RN) is a symmetric matrix for all t ∈ R, B = [bij] is an antisymmetric N × N constant matrix, and H(t, x) ∈ C 1 (R × Bδ , R) i...
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Dokumentumtípus: | Folyóirat |
Megjelent: |
2022
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Sorozat: | Electronic journal of qualitative theory of differential equations
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Kulcsszavak: | Differenciálegyenlet |
Tárgyszavak: | |
Online Access: | http://acta.bibl.u-szeged.hu/78352 |
Tartalmi kivonat: | In this paper, we consider the multiplicity of homoclinic solutions for the following damped vibration problems x¨(t) + Bx˙(t) − A(t)x(t) + Hx(t, x(t)) = 0, where A(t) ∈ (R, RN) is a symmetric matrix for all t ∈ R, B = [bij] is an antisymmetric N × N constant matrix, and H(t, x) ∈ C 1 (R × Bδ , R) is only locally defined near the origin in x for some δ > 0. With the nonlinearity H(t, x) being partially sub-quadratic at zero, we obtain infinitely many homoclinic solutions near the origin by using a Clark’s theorem. |
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ISSN: | 1417-3875 |