We discuss the multiplicity of nonnegative solutions of a parametric one-dimensional mean curvature problem. Our main effort here is to describe the configuration of the limits of a certain function, depending on the potential at zero, that yield, for certain values of the parameter, the existence of infinitely many weak nonnegative and nontrivial solutions. Moreover, thanks to a classical regularity result due to Lieberman, this sequence of solutions strongly converges to zero in C^1 ([0, 1]). Our approach is based on recent variational methods.

A variational approach for one-dimensional prescribed mean curvature problems

Molica Bisci G
2014-01-01

Abstract

We discuss the multiplicity of nonnegative solutions of a parametric one-dimensional mean curvature problem. Our main effort here is to describe the configuration of the limits of a certain function, depending on the potential at zero, that yield, for certain values of the parameter, the existence of infinitely many weak nonnegative and nontrivial solutions. Moreover, thanks to a classical regularity result due to Lieberman, this sequence of solutions strongly converges to zero in C^1 ([0, 1]). Our approach is based on recent variational methods.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11576/2664344
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