Asymptotically linear problems driven by fractional Laplacian operators. (16th April 2015)

• Record Type: Journal Article
• Authors: Fiscella, Alessio; Servadei, Raffaella; Valdinoci, Enrico
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 16(2015:Nov. 15)
• Page Start: 3551
• Page End: 3563
• Publication Date: 2015-04-16
• Subjects: integrodifferential operators -- fractional Laplacian -- variational techniques -- Saddle Point Theorem -- Palais–Smale condition; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3438
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we study a non‐local fractional Laplace equation, depending on a parameter, with asymptotically linear right‐hand side. Our main result concerns the existence of weak solutions for this equation, and it is obtained using variational and topological methods. We treat both the non‐resonant case and the resonant one. Copyright © 2015 John Wiley & Sons, Ltd.