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Kirchhoff Equations with Choquard Exponential Type Nonlinearity Involving the Fractional Laplacian
Published in
Volume: 172
Issue: 1
In this article, we deal with the existence of non-negative solutions of the class of following non local problem {−M(∫Rn∫Rn|u(x)−u(y)|ns|x−y|2ndxdy)(−Δ)n/ssu=(∫ΩG(y,u)|x−y|μdy)g(x,u)inΩ,u=0inRn∖Ω, where (−Δ)n/ss is the n/ s-fractional Laplace operator, n≥ 1 , s∈ (0 , 1) such that n/ s≥ 2 , Ω ⊂ Rn is a bounded domain with Lipschitz boundary, M: R+→ R+ and g: Ω × R→ R are continuous functions, where g behaves like exp(|u|nn−s) as | u| → ∞. The key feature of this article is the presence of Kirchhoff model along with convolution type nonlinearity having exponential growth which appears in several physical and biological models. © 2021, The Author(s), under exclusive licence to Springer Nature B.V.}, author_keywords={Choquard nonlinearity; Doubly non local problems; Kirchhoff equation; Trudinger-Moser nonlinearity}, keywords={Applications; Mathematical techniques, Biological models; Continuous functions; Exponential growth; Fractional Laplacian; Kirchhoff equation; Lipschitz boundary; Non-negative solutions; Nonlocal problems, Laplace transforms}, funding_details={Department of Science and Technology, Ministry of Science and Technology, IndiaDepartment of Science and Technology, Ministry of Science and Technology, India, डीएसटी, ECR/2017/002651}, funding_details={Science and Engineering Research BoardScience and Engineering Research Board, SERB}, funding_text_1={This research is supported by Science and Engineering Research Board, Department of Science and Technology, Government of India, Grant number: ECR/2017/002651. The second author wants to thank Bennett University for its hospitality during her visit there.}, funding_text_2={This research is supported by Science and Engineering Research Board, Department of Science and Technology, Government of India, Grant number: ECR/2017/002651. The second author wants to thank Bennett University for its hospitality during her visit there.}, references={Alves, C.O., Yang, M., Existence of solutions for a nonlocal variational problem in R2 with exponential critical growth (2017) J. Convex Anal., 24 (4), pp. 1197-1215; Alves, C.O., Cassani, D., Tarsi, C., Yang, M., Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in R2 (2016) J. Differ. Equ., 261 (3), pp. 1933-1972; Applebaum, D., Lévy processes—from probability to finance and quantum groups (2004) Not. Am. Math. 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Equ., 58 (2)}, correspondence_address1={Mukherjee, T.; Department of Mathematics, India; email: tulimukh@gmail.com}, publisher={Springer Science and Business Media B.V.}, issn={01678019}, coden={AAMAD}, language={English}, abbrev_source_title={Acta Appl Math}, document_type={Article}, source={Scopus},
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JournalActa Applicandae Mathematicae