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Existence of multiple solutions for a wide class of differential inclusions

Author

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  • Filomena Cianciaruso
  • Paolamaria Pietramala

Abstract

We give a unified approach to study the existence of multiple positive solutions of nonlinear differential inclusions of the form −u′′(t)∈F(t,u(t)),a.e.t∈(0,1),$$\begin{equation*}\hskip7pc -u^{\prime \prime }(t)\in F(t,u(t)),\; \text{a.e.} \; t \in (0,1), \end{equation*}$$subject to various nonlocal boundary conditions. We study these problems via a perturbed integral inclusion of the form u(t)∈Bu(t)+∫01k(t,s)F(s,u(s))ds$ u(t)\in Bu(t) +\int _{0}^{1}k(t,s)F(s,u(s))\,ds$.

Suggested Citation

  • Filomena Cianciaruso & Paolamaria Pietramala, 2023. "Existence of multiple solutions for a wide class of differential inclusions," Mathematische Nachrichten, Wiley Blackwell, vol. 296(1), pages 152-163, January.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:1:p:152-163
    DOI: 10.1002/mana.202100385
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    References listed on IDEAS

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    1. Gennaro Infante, 2021. "Nontrivial Solutions of Systems of Perturbed Hammerstein Integral Equations with Functional Terms," Mathematics, MDPI, vol. 9(4), pages 1-9, February.
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