On boundary-value problems for second order perturbed differential inclusions

Dhage, B. C.; Graef, John R.

doi:10.1080/00036810500136197

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Cited by 7 publications

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“…\; t \in (0,1), \end{equation}$$where F is a nonnegative Carathéodory multifunction and the nonlocal boundary conditions involving linear functionals on C [0, 1], namely,

\begin{equation} a_1u(0)-b_1u^{\prime }(0)=\alpha [u], \;\;a_2u(1)+b_2u^{\prime }(1)=\beta [u]. \end{equation}

Differential inclusions have received attention in various contests, see for example, [1, 6, 11–14, 17, 21, 23, 32, 33]. They arise in the study of problems in applied mathematics, engineering, and economics, since some mathematical models utilize multivalued maps [3, 9].…”

Section: Introductionmentioning

confidence: 99%

Existence of multiple solutions for a wide class of differential inclusions^†

Cianciaruso

Pietramala

2022

Mathematische Nachrichten

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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), subject to various nonlocal boundary conditions. We study these problems via a perturbed integral inclusion of the form 𝑢(𝑡) ∈ 𝐵𝑢(𝑡) + ∫ 1 0 𝑘(𝑡, 𝑠)𝐹(𝑠, 𝑢(𝑠)) 𝑑𝑠.

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“…\; t \in (0,1), \end{equation}$$where F is a nonnegative Carathéodory multifunction and the nonlocal boundary conditions involving linear functionals on C [0, 1], namely,