Solvability of a Class of Fractional Advection–Dispersion Coupled Systems

Yan Qiao () and Tao Lu
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Yan Qiao: School of Mathematical Sciences, Jiangsu Second Normal University, Nanjing 211200, China
Tao Lu: School of Mathematical Sciences, Jiangsu Second Normal University, Nanjing 211200, China

Mathematics, 2024, vol. 12, issue 18, 1-18

Abstract: The purpose of this study is to provide some criteria for the existence and multiplicity of solutions for a class of fractional advection–dispersion coupled systems with nonlinear Sturm–Liouville conditions and instantaneous and non-instantaneous impulses. Specifically, the existence is derived through the Nehari manifold method, and the proof of multiplicity is based on Bonanno and Bisci’s critical point theorem, which does not require proof that the functional satisfies the Palais–Smale condition. Finally, to illustrate the obtained results, an example is provided.

Keywords: fractional advection–dispersion coupled system; instantaneous and non-instantaneous impulses; nonlinear Sturm–Liouville conditions; Nehari manifold; critical point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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