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Existence of solutions for a two point boundary value problem

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Abstract

We consider the two point boundary value problemF[y]=y″−f(x,y,y′)=0,a≤x≤b, y(a)=A, y(b)=B. Assuming thatf satisfies certain differential inequalities associated with the existence ofF-subfunctions andF-superfunctions, and thatf also satisfies a suitable growth condition with respect toy′, we prove that the two point boundary value problem has a solutiony with (x, y(x), y′(x)) in a specified region; indeed we show that the problem has a maximal and a minimal solution in this region. Our results unify and generalize earlier results of K. Ako, L. K. Jackson, M. Nagumo, and others.

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Authors and Affiliations

  1. Department of Mathematics, University of Queensland, 4067, St. Lucia, Q'ld., Australia

    H. B. Thompson

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  1. H. B. Thompson
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Thompson, H.B. Existence of solutions for a two point boundary value problem. Rend. Circ. Mat. Palermo 35, 261–275 (1986). https://doi.org/10.1007/BF02844736

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  • DOI: https://doi.org/10.1007/BF02844736

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