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A la recherche du spectre perdu: An invitation to nonlinear spectral theory

Appell, Jürgen (2003)

Nonlinear Analysis, Function Spaces and Applications

We give a survey on spectra for various classes of nonlinear operators, with a particular emphasis on a comparison of their advantages and drawbacks. Here the most useful spectra are the asymptotic spectrum by M. Furi, M. Martelli and A. Vignoli (1978), the global spectrum by W. Feng (1997), and the local spectrum (called “phantom”) by P. Santucci and M. Väth (2000). In the last part we discuss these spectra for homogeneous operators (of any degree), and derive a discreteness result and a nonlinear...

A note on solutions of semilinear equations at resonance in a cone

Bogdan Przeradzki (1993)

Annales Polonici Mathematici

A connection between the Landesman-Lazer condition and the solvability of the equation Lx = N(x) in a cone with a noninvertible linear operator L is studied. The result is based on the abstract framework from [5], applied to the existence of periodic solutions of ordinary differential equations, and compared with theorems by Santanilla (see [7]).

A Random Evolution Inclusion of Subdifferential Type in Hilbert Spaces

Kravvaritis, D., Pantelidis, G. (1996)

Serdica Mathematical Journal

In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6].

A refined Newton’s mesh independence principle for a class of optimal shape design problems

Ioannis Argyros (2006)

Open Mathematics

Shape optimization is described by finding the geometry of a structure which is optimal in the sense of a minimized cost function with respect to certain constraints. A Newton’s mesh independence principle was very efficiently used to solve a certain class of optimal design problems in [6]. Here motivated by optimization considerations we show that under the same computational cost an even finer mesh independence principle can be given.

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