On nonlocal Dirichlet problems with oscillating term

Boštjan Gabrovšek; Giovanni Molica Bisci; Dušan D. Repovš

doi:10.3934/dcdss.2022130

Article Contents

2023, Volume 16, Issue 6: 1401-1413. Doi: 10.3934/dcdss.2022130

This issue Previous Article Blow-up and lifespan estimate for wave equations with critical damping term of space-dependent type related to Glassey conjecture Next Article Singular equations with variable exponents and concave-convex nonlinearities

On nonlocal Dirichlet problems with oscillating term

1.
Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, 1000, Slovenia
2.
Dipartimento di Scienze Pure e Applicate (DiSPeA), Università degli Studi di Urbino Carlo Bo, Urbino, 61029, Italy
3.
Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, 1000, Slovenia

^* Corresponding author: Giovanni Molica Bisci
^* Corresponding author: Giovanni Molica Bisci

Dedicated to the loving memory of Gaetana Restuccia

Received: April 2021

Revised: May 2022

Early access: June 2022

Published: June 2023

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Abstract

In this paper, a class of nonlocal fractional Dirichlet problems is studied. By using a variational principle due to Ricceri (whose original version was given in J. Comput. Appl. Math. 113 (2000), 401–410), the existence of infinitely many weak solutions for these problems is established by requiring that the nonlinear term $ f $ has a suitable oscillating behaviour either at the origin or at infinity.

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Mathematics Subject Classification: Primary: 47J30, 35R11; Secondary: 35S15, 35A15.

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References

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