Asymptotically linear problems driven by fractional Laplacian operators

Alessio Fiscella; Raffaella Servadei; Enrico Valdinoci

doi:10.1002/mma.3438

Asymptotically linear problems driven by fractional Laplacian operators

Alessio Fiscella
, Raffaella Servadei
, Enrico Valdinoci

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

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.

Original language	English
Pages (from-to)	3551-3563
Number of pages	13
Journal	Mathematical Methods in the Applied Sciences
Volume	38
Issue number	16
DOIs	https://doi.org/10.1002/mma.3438
Publication status	Published - 1 Jan 2015
Externally published	Yes

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10.1002/mma.3438

https://web.ma.utexas.edu/mp_arc/c/12/12-128.pdf?

Cite this

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title = "Asymptotically linear problems driven by fractional Laplacian operators",

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.",

keywords = "fractional Laplacian, integrodifferential operators, Palais-Smale condition, Saddle Point Theorem, variational techniques",

author = "Alessio Fiscella and Raffaella Servadei and Enrico Valdinoci",

year = "2015",

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T1 - Asymptotically linear problems driven by fractional Laplacian operators

AU - Fiscella, Alessio

AU - Servadei, Raffaella

AU - Valdinoci, Enrico

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

KW - fractional Laplacian

KW - integrodifferential operators

KW - Palais-Smale condition

KW - Saddle Point Theorem

KW - variational techniques

UR - https://www.scopus.com/pages/publications/84945479139

U2 - 10.1002/mma.3438

DO - 10.1002/mma.3438

M3 - Article

AN - SCOPUS:84945479139

SN - 0170-4214

VL - 38

SP - 3551

EP - 3563

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 16

ER -

Asymptotically linear problems driven by fractional Laplacian operators

Abstract

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