Abstract
We discuss the dependence of solutions on functional parameters for a certain class of systems of Sturm–Liouville equations. We consider the problems in which parameters appear in the differential operator as well as in the nonlinearity. This result will be proved without any assumptions concerning the uniqueness of solutions. Our approach covers both sublinear and superlinear cases. Finally, we apply these results to formulate sufficient conditions for a certain optimal control problem.
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Orpel, A. Systems of nonlinear Sturm–Liouville problems – the dependence of solutions on functional parameters. Acta Math. Hungar. 146, 247–260 (2015). https://doi.org/10.1007/s10474-015-0508-7
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DOI: https://doi.org/10.1007/s10474-015-0508-7
Key words and phrases
- Sturm–Liouville equation
- positive solution
- continuous dependence of solutions on functional parameters