General Letters in Mathematics

Volume 3 - Issue 3 (2) | PP: 154 - 163 Language : English
DOI : https://doi.org/DOI:10.31559/glm2016.3.3.2
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Multiple Homoclinic Solutions for a Class of Superquadratic Fourth-order Differential Equations

Mohsen Timoumi
Received Date Revised Date Accepted Date Publication Date
28/10/2017 16/11/2017 25/12/2017 9/1/2018
Abstract
Applying a Symmetric Mountain Pass Theorem, we prove the existence of infinitely many homoclinic solutions for a class of fourth-order differential equations u(4)(x) + ωu00(x) + a(x)u(x) = f(x,u(x)), ∀x ∈R where a ∈ C(R,R) may be negative on a bounded interval and F(x,u) =Ru 0 f(x,t)dt is superquadratic at infinity in the second variable but does not need to satisfy the well-known Ambrosetti-Rabinowitz superquadratic growth condition.


How To Cite This Article
Timoumi , M. (2018). Multiple Homoclinic Solutions for a Class of Superquadratic Fourth-order Differential Equations . General Letters in Mathematics, 3 (3), 154-163, DOI:10.31559/glm2016.3.3.2

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