Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities

Nikolaos Papageorgiou; Francesca Papalini

Annales Polonici Mathematici (2000)

  • Volume: 75, Issue: 2, page 125-141
  • ISSN: 0066-2216

Abstract

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We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.

How to cite

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Papageorgiou, Nikolaos, and Papalini, Francesca. "Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities." Annales Polonici Mathematici 75.2 (2000): 125-141. <http://eudml.org/doc/208390>.

@article{Papageorgiou2000,
abstract = {We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.},
author = {Papageorgiou, Nikolaos, Papalini, Francesca},
journal = {Annales Polonici Mathematici},
keywords = {eigenvalues; multivalued problem; discontinuous term; p-Laplacian; subdifferential; locally Lipschitz functional},
language = {eng},
number = {2},
pages = {125-141},
title = {Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities},
url = {http://eudml.org/doc/208390},
volume = {75},
year = {2000},
}

TY - JOUR
AU - Papageorgiou, Nikolaos
AU - Papalini, Francesca
TI - Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities
JO - Annales Polonici Mathematici
PY - 2000
VL - 75
IS - 2
SP - 125
EP - 141
AB - We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.
LA - eng
KW - eigenvalues; multivalued problem; discontinuous term; p-Laplacian; subdifferential; locally Lipschitz functional
UR - http://eudml.org/doc/208390
ER -

References

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  8. [8] D. G. De Figueiredo, On the existence of multiple ordered solutions of nonlinear eigenvalue problems, ibid. 11 (1987), 481-492. Zbl0661.35070
  9. [9] D. Goeleven, D. Motreanu and P. D. Panagiotopoulos, Multiple solutions for a class of eigenvalue problems in hemivariational inequalities, ibid. 29 (1997), 9-26. Zbl0878.49009
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  11. [11] N. C. Kurogenis and N. S. Papageorgiou, Nonsmooth critical point theory and nonlinear elliptic equations at resonance, to appear. 
  12. [12] C. Lefter and D. Motreanu, Critical Points Methods in Nonlinear Eigenvalue Problems with Discontinuities, Internat. Ser. Numer. Math. 107, Birkhäuser, Basel, 1992. Zbl0802.35115
  13. [13] P. Lindqvist, On the equations d i v ( ∥ D x ∥ p - 2 D x ) + λ | x | p - 2 x = 0 , Proc. Amer. Math. Soc. 109 (1990), 157-164. 
  14. [14] P. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Partial Differential Equations, CBMS Regional Conf. Ser. in Math. 65, Amer. Math. Soc., Providence, RI, 1986. Zbl0609.58002
  15. [15] M. Ramos, A critical point theorem suggested by an elliptic problem with asymmetric nonlinearities, J. Math. Anal. Appl. 196 (1995), 938-946. Zbl0853.58032
  16. [16] E. Zeidler, Nonlinear Functional Analysis and its Applications, Springer, New York, 1985. Zbl0583.47051

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