Multiple Homoclinic Solutions for a Class of Superquadratic Fourth-order Differential Equations

Multiple Homoclinic Solutions for a Class of Superquadratic Fourth-order Differential Equations

Volume 3, Issue 3, Article 2 - 2017

Authors: Mohsen Timoumi

Copyright © 2017 . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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

@article{Timoumi_2017, doi = {10.31559/glm2016.3.3.2}, url = {https://doi.org/10.31559%2Fglm2016.3.3.2}, year = 2017, month = {dec}, publisher = {Refaad for Studies and Research}, volume = {3}, number = {3}, author = {Mohsen Timoumi}, title = {Multiple Homoclinic Solutions for a Class of Superquadratic Fourth-order Differential Equations}, journal = {General Letters in Mathematics} }
Timoumi, M. (2017). Multiple Homoclinic Solutions for a Class of Superquadratic Fourth-order Differential Equations. General Letters in Mathematics, 3(3). doi:10.31559/glm2016.3.3.2
[1]M. Timoumi, “Multiple Homoclinic Solutions for a Class of Superquadratic Fourth-order Differential Equations,” General Letters in Mathematics, vol. 3, no. 3, Dec. 2017.
Timoumi, Mohsen. “Multiple Homoclinic Solutions for a Class of Superquadratic Fourth-Order Differential Equations.” General Letters in Mathematics 3, no. 3 (December 1, 2017). doi:10.31559/glm2016.3.3.2.