A characterization of generalized inner product spaces (?-orthogonally additive mappings, III).
A DSM proof of surjectivity of monotone nonlinear mappings
A simple proof is given of a basic surjectivity result for monotone operators. The proof is based on the dynamical systems method (DSM).
A fixed point theorem
A fixed point theorem for multivalued mappings.
A general separation theorem for mappings, saddle-points duality and conjugate functions
A generalization of Krasnoseljski's fixed point theorem in probabilistic locally convex spaces
A generalization of the interior mapping theorem of Clarke and Pourciau
A generalization of the Landesman-Lazer condition.
A global description of solutions to nonlinear perturbations of the Wiener--Hopf integral equations.
A global index for bifurcation of fixed points.
A la recherche du spectre perdu: An invitation to nonlinear spectral theory
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 nonlinear operator in potential theory
A note on solutions of semilinear equations at resonance in a cone
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 note on the existence of more than one solution for asymptotically linear equations
A one dimensional Hammerstein problem.
A Random Evolution Inclusion of Subdifferential Type in Hilbert Spaces
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 rapid convergence method for a singular perturbation problem
A refined Newton’s mesh independence principle for a class of optimal shape design problems
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.
A remark on recent results for finding zeroes of accretive operators.
A remark on small divisors problems