Region of existence of multiple solutions for a class of robin type four-point bvps

This article aims to prove the existence of a solution and compute the region of existence for a class of four-point nonlinear boundary value problems (NLBVPs) defined as [formula] where I = [0, 1], 0 < ξ≥ η < 1 and λ 1 ,λ > 0. The nonlinear source term [formula] is one sided Lipschitz in u’ with Lipschitz constant L 1 and Lipschitz in u', such that [formula]. We develop monotone iterative technique (MI-technique) in both well ordered and reverse ordered cases. We prove maximum, anti-maximum principle under certain assumptions and use it to show the monotonic behaviour of the sequences of upper-lower solutions. The sufficient conditions are derived for the existence of solution and verified for two examples. The above NLBVPs is linearised using Newton’s quasilinearization method which involves a parameter k equivalent to max [formula]. We compute the range of k for which iterative sequences are convergent.

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Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).