Existence and multiplicity of solutions involving the $p(x)$-Laplacian equations : on the effect of two nonlocal terms

Hamdani, Mohamed Karim (author), Mbarki, Lamine (author), Allaoui, Mostafa (author), Darhouche, Omar (author), Repovš, Dušan (author)

We study a class of $p(x)$-Kirchhoff problems which is seldom studied because the nonlinearity has nonstandard growth and contains a bi-nonlocal term. Based on variational methods, especially the Mountain pass theorem and Ekeland's variational principle, we obtain the existence of two nontrivial solutions for the problem under certain assumptions. We also apply the Symmetric mountain pass theorem and Clarke's theorem to establish the existence of infinitely many solutions. Our results generalize and extend several existing results.

• Language: English
• Keywords: p(x)-Laplacian operator, variational methods, Kirchhoff problem, bi-nonlocal term, Ambrosetti-Rabinowitz condition
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: Str. 1452-1467
• Numbering: Vol. 16, no. 6
• PID: 20.500.12556/RUL-146300-326aaeea-7989-830d-ef04-3608f442c807
• UDC: 517.956
• ISSN on article: 1937-1632
• DOI: 10.3934/dcdss.2022129
• COBISS.SI-ID: 111490051

Copyright

Založnikova različica članka je v RUL shranjena v skladu z založnikovo pogodbo z avtorji. (Datum opombe: 24. 5. 2023)

• Publication date in RUL: 23.05.2023

Record is a part of a journal

• Title: Discrete and continuous dynamical systems. Series S
• Shortened title: Discret. contin. dyn. syst., Ser. S
• Publisher: American Institute of Mathematical Sciences
• ISSN: 1937-1632
• COBISS.SI-ID: 16098905