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

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

Mathematics, 2020, vol. 8, issue 4, 1-10

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.

Keywords: homoclinic solutions; fourth-order p-Laplacian differential equations; minimization theorem; Clark’s theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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