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Infinitely Many Homoclinic Solutions for Fourth Order p-Laplacian Differential Equations

Author

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  • Stepan Tersian

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (BAS), 1113 Sofia, Bulgaria)

Abstract

The existence of infinitely many homoclinic solutions for the fourth-order differential equation φ p u ″ t ″ + w φ p u ′ t ′ + V ( t ) φ p u t = a ( t ) f ( t , u ( t ) ) , t ∈ R is studied in the paper. Here φ p ( t ) = t p − 2 t , p ≥ 2 , w is a constant, V and a are positive functions, f satisfies some extended growth conditions. Homoclinic solutions u are such that u ( t ) → 0 , | t | → ∞ , u ≠ 0 , known in physical models as ground states or pulses. The variational approach is applied based on multiple critical point theorem due to Liu and Wang.

Suggested Citation

  • Stepan Tersian, 2020. "Infinitely Many Homoclinic Solutions for Fourth Order p-Laplacian Differential Equations," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:505-:d:340501
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    References listed on IDEAS

    as
    1. Li, Tiexiang & Sun, Juntao & Wu, Tsung-fang, 2015. "Existence of homoclinic solutions for a fourth order differential equation with a parameter," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 499-506.
    2. Zhang, Ziheng & Yuan, Rong, 2015. "Homoclinic solutions for a nonperiodic fourth order differential equations without coercive conditions," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 280-286.
    3. Liu Yang, 2014. "Infinitely Many Homoclinic Solutions for Nonperiodic Fourth Order Differential Equations with General Potentials," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, June.
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