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On a Nonlocal BVP with Nonlinear Boundary Conditions

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Abstract

We consider the existence of at least one positive solution of the problem \({-y''(t)=f(t,y(t)), y(0)=H_1(\varphi(y))+\int_{E}H_2(s,y(s))\,ds, y(1)=0}\), where \({y(0)=H_1(\varphi(y))+\int_{E}H_2(s,y(s))\,ds}\) represents a nonlinear, nonlocal boundary condition. We show by imposing some relatively mild structural conditions on f, H 1, H 2, and \({\varphi}\) that this problem admits at least one positive solution. Finally, our results generalize and improve existing results, and we give a specific example illustrating these generalizations and improvements.

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  1. Creighton Preparatory School, 7400 Western Ave., Omaha, NE, 68114, USA

    Christopher S. Goodrich

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  1. Christopher S. Goodrich
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Correspondence to Christopher S. Goodrich.

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Goodrich, C.S. On a Nonlocal BVP with Nonlinear Boundary Conditions. Results. Math. 63, 1351–1364 (2013). https://doi.org/10.1007/s00025-012-0272-8

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  • DOI: https://doi.org/10.1007/s00025-012-0272-8

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