On a Nonlocal BVP with Nonlinear Boundary Conditions |
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Authors: | Christopher S Goodrich |
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Institution: | 1. Creighton Preparatory School, 7400 Western Ave., Omaha, NE, 68114, USA
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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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