On nonlocal Dirichlet problems with oscillating term-Reference-Cited by-同舟云学术

On nonlocal Dirichlet problems with oscillating term

Published:2022 Issue:0 Volume:0 Page:0
ISSN:1937-1632
Container-title:Discrete and Continuous Dynamical Systems - S
language:
Short-container-title:DCDS-S

Author:

Gabrovšek Boštjan¹,Bisci Giovanni Molica²,Repovš Dušan D.³

Affiliation:

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

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ f $\end{document}</tex-math></inline-formula> has a suitable oscillating behaviour either at the origin or at infinity.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference31 articles.

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2. V. Ambrosio, L. D'Onofrio, and G. Molica Bisci.On nonlocal fractional Laplacian problems with oscillating potentials, Rocky Mountain J. Math., 48 (2018), 1399-1436.

3. G. Bonanno, G. Molica Bisci.Infinitely many solutions for a Dirichlet problem involving the $p$–Laplacian, Proc. Roy. Soc. Edinburgh Sect. A, 140 (2010), 737-752.

4. L. M. Del Pezzo, A. Quaas.A Hopf's lemma and a strong minimum principle for the fractional $p$-Laplacian, J. Differential Equations, 263 (2017), 765-778.

5. F. Demengel and G. Demengel, Functional Spaces for the Theory of Elliptic Partial Differential Equations, Springer, Berlin, 2012.

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