Multiple Positive Solutions for Eigenvalue Problems of Hemivariational Inequalities

Multiple Positive Solutions for Eigenvalue Problems of Hemivariational Inequalities We study a nonlinear eigenvalue problem with a nonsmooth potential. The subgradients of the potential are only positive near the origin (from above) and near +∞. Also the subdifferential is not necessarily monotone (i.e. the potential is not convex). Using variational techniques and the method of upper and lower solutions, we establish the existence of at least two strictly positive smooth solutions for all the parameters in an interval. Our approach uses the nonsmooth critical point theory for locally Lipschitz functions. A byproduct of our analysis is a generalization of a result of Brezis-Nirenberg (CRAS, 317 (1993)) on H 1 0 versus C 1 0 minimizers of a C 1-functional. Positivity Springer Journals

Multiple Positive Solutions for Eigenvalue Problems of Hemivariational Inequalities

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Copyright © 2006 by Birkhäuser Verlag, Basel
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
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