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Smooth continuation of solutions and eigenvalues for variational inequalities based on the implicit function theorem |
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| Authors: | Jan Eisner Milan Ku?era Lutz Recke |
| Institution: | a Mathematical Institute of the Academy of Sciences of the Czech Republic, ?itná 25, 115 67 Prague 1, Czech Republic b Centre of Applied Mathematics, Faculty of Applied Sciences, University of West Bohemia, 306 14 Plzeň, Czech Republic c Institute of Mathematics of the Humboldt University of Berlin, Unter den Linden 6, 10099 Berlin, Germany |
| Abstract: | The implicit function theorem is applied in a nonstandard way to abstract variational inequalities depending on a (possibly infinite-dimensional) parameter. In this way, results on smooth continuation of solutions as well as of eigenvalues and eigenvectors are established under certain particular assumptions. The abstract results are applied to a linear second order elliptic eigenvalue problem with nonlocal unilateral boundary conditions (Schrödinger operator with the potential as the parameter). |
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