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

• Autorzy: Verma Amit K. , Urus Nazia , Agarwal Ravi P.

Identyfikatory

DOI

10.7494/OpMath.2021.41.4.571

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Green’s function; monotone iterative technique; maximum principle; multi-point problem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2021
• Tom: Vol. 41, no. 4
• Strony: 571--600
• Opis fizyczny: Bibliogr. 54 poz.

Twórcy

autor

Verma Amit K.

• IIT Patna Department of Mathematics Bihta, Patna 801103, (BR) India

• https://orcid.org/0000-0001-8768-094X

autor

Urus Nazia

• IIT Patna Department of Mathematics Bihta, Patna 801103, (BR) India

• https://orcid.org/0000-0001-8456-1806

autor

Agarwal Ravi P.

• Texas A&M, University-Kingsville Department of Mathematics 700 University Blvd., MSC 172, Kingsville, TX 78363-8202, USA

• https://orcid.org/0000-0003-0634-2370

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Uwagi

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