Title
Infinitely many solutions for a nonlocal type problem with sign-changing weight function
Date Issued
2021
Access level
metadata only access
Resource Type
journal article
Author(s)
Publisher(s)
Texas State University - San Marcos
Abstract
In this article, we study the existence of weak solutions for a fractional type problem driven by a nonlocal operator of elliptic type (Formula Presented) Our approach is based on critical point theorems and variational methods.
Start page
1
End page
15
Volume
2021
Language
English
OCDE Knowledge area
Matemáticas puras
Subjects
Scopus EID
2-s2.0-85103598559
Source
Electronic Journal of Differential Equations
ISSN of the container
10726691
Sponsor(s)
Using that φ1− > 1, the above inequality shows that {un} is bounded in W0sLΦ1(Ω). From Lemma 3.6, we obtain the desired assertion. □ Proof Theorem 1.2. By (A3) f is odd, then Jλ is an even functional. From Lemmas 3.8 and 3.9, the functional Jλ satisfies all the conditions of the Fountain theorem 2.16 Hence, Jλ has an unbounded sequence of critical values, that is there exists a sequence {un} ⊂ W0sLΦ1(Ω) such that Jλ′(uk) = 0 and Jλ(uk) → ∞ as k → ∞. This completes the proof. □ Acknowledgments. The authors warmly thank the anonymous referee for her/his useful comments on the paper. C. Torres was partially supported by CONCYTEC PIBA 2019 - I, Contrato N◦ 379-2019-2019-FONDECYT
Sources of information:
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