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Open AccessFeature PaperArticle

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

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (BAS), 1113 Sofia, Bulgaria
Mathematics 2020, 8(4), 505; https://doi.org/10.3390/math8040505
Received: 17 March 2020 / Revised: 31 March 2020 / Accepted: 1 April 2020 / Published: 2 April 2020
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. View Full-Text
Keywords: homoclinic solutions; fourth-order p-Laplacian differential equations; minimization theorem; Clark’s theorem homoclinic solutions; fourth-order p-Laplacian differential equations; minimization theorem; Clark’s theorem
MDPI and ACS Style

Tersian, S. Infinitely Many Homoclinic Solutions for Fourth Order p-Laplacian Differential Equations. Mathematics 2020, 8, 505.

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