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On the Existence of Nonautonomous ODE with Application to Semilinear Elliptic Equations

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Abstract

We prove an existence result for a second-order nonautonomous nonlinear ordinary differential equation with a particular asymptotic behavior. This solution is then proved to be a limiting profile for a semilinear elliptic equation on the quarter plane. Our results are mainly based upon the maximum principle; the method of sub- and super-solutions and the sliding method.

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Acknowledgements

The authors are indebted to an anonymous referee for his extensive comments that improved the final presentation of the paper. This project has been funded with support from the Lebanese University.

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  1. Mathematics Department, Faculty of Sciences, Branch 1, Lebanese University, Hadath, Lebanon

    Hassan Ibrahim & Elissar Nasreddine

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  1. Hassan Ibrahim
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  2. Elissar Nasreddine
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Correspondence to Hassan Ibrahim.

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Ibrahim, H., Nasreddine, E. On the Existence of Nonautonomous ODE with Application to Semilinear Elliptic Equations. Mediterr. J. Math. 15, 64 (2018). https://doi.org/10.1007/s00009-018-1112-1

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  • DOI: https://doi.org/10.1007/s00009-018-1112-1

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