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

Neumann, Jan

Commentat. Math. Univ. Carol. 28, 277-293 (1987).

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

Keywords:

eigenvalue problems; variational inequalities; bifurcation; abstract ordinary differential inequality