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**An abstract differential inequality and eigenvalues of variational inequalities.**
*(English)*
Zbl 0636.35011

Another proof of a theorem by E. Miersemann [On higher eigenvalues of variational inequalities, Commentat. Math. Univ. Carol. 24, 657-665 (1983)] concerning eigenvalue problems for variational inequalities is given. The author claims that his method was suggested by some ideas used by I. V. Skrypnik to prove bifurcation results for variational inequalities. Section 1 includes a careful study of solutions for an abstract ordinary differential inequality and Section 2 contains the proof of the theorem. The link between both is that the eigenvalue for the variational inequality is obtained as a limit value (for \(t\to \infty)\) of a solution of the differential inequality for a suitable initial condition.

Reviewer: J.Hernandez

### MSC:

35B32 | Bifurcations in context of PDEs |

35P30 | Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs |

49J40 | Variational inequalities |

34G20 | Nonlinear differential equations in abstract spaces |

58E07 | Variational problems in abstract bifurcation theory in infinite-dimensional spaces |

58E35 | Variational inequalities (global problems) in infinite-dimensional spaces |