Refaad for Studies, Research and Developement
Multiple Homoclinic Solutions for a Class of Superquadratic Fourthorder Diﬀerential Equations
25199269 (Print)
25199277 (Online)
Volume 3
Issue 3
2017

0
Multiple Homoclinic Solutions for a Class of Superquadratic Fourthorder Diﬀerential Equations
154
163
English
Mohsen TimoumiFaculty of Sciences.Dpt of Mathematics, 5000 Monastir. Tunisia m_timoumi@yahoo.com
Applying a Symmetric Mountain Pass Theorem, we prove the existence of inﬁnitely many homoclinic solutions for a class of fourthorder 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 wellknown AmbrosettiRabinowitz superquadratic growth condition
Fourthorder diﬀerential equation; homoclinic solutions; variational methods; Symmetric Mountain Pass Theorem
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http://www.refaad.com/Files/GLM/GLM332.pdf