Eigenwertaussagen für kompakte und kondensierende mengenwertige Abbildungen in topologischen Vektorräumen
Ein „merkwürdiges” Spektrum für nichtlineare Operatoren
We define a spectrum for Lipschitz continuous nonlinear operators in Banach spaces by means of a certain kind of "pseudo-adjoint" and study some of its properties.
Equivalent solutions of nonlinear equations in a topological vector space with a wedge.
Existence, multiplicity, and bifurcation in systems of ordinary differential equations.
Existence of a ray of eigenvalues for equations with discontinuous operators.
Fixed point free maps of a closed ball with small measures of noncompactness.
We show that in all infinite-dimensional normed spaces it is possible to construct a fixed point free continuous map of the unit ball whose measure of noncompactness is bounded by 2. Moreover, for a large class of spaces (containing separable spaces, Hilbert spaces and l-infinity (S)) even the best possible bound 1 is attained for certain measures of noncompactness.
Fixed points, eigenvalues and surjectivity for (ws)-compact operators on unbounded convex sets
The paper studies the existence of fixed points for some nonlinear (ws)-compact, weakly condensing and strictly quasibounded operators defined on an unbounded closed convex subset of a Banach space. Applications of the newly developed fixed point theorems are also discussed for proving the existence of positive eigenvalues and surjectivity of quasibounded operators in similar situations. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness.
Four-parameter bifurcation for a -Laplacian system.
Generalized communication conditions and the eigenvalue problem for a monotone and homogenous function
This work is concerned with the eigenvalue problem for a monotone and homogenous self-mapping of a finite dimensional positive cone. Paralleling the classical analysis of the (linear) Perron–Frobenius theorem, a verifiable communication condition is formulated in terms of the successive compositions of , and under such a condition it is shown that the upper eigenspaces of are bounded in the projective sense, a property that yields the existence of a nonlinear eigenvalue as well as the projective...
Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity
Isoperimetric inequalities for some nonlinear eigenvalue problems.
Multiple eigenvalue bifurcation for Fredholm operators.
Non-linear eigenvalue problems and bifurcations for differentiable multivalued maps
Nonlinear Spectral Theories and Solvability of Nonlinear Hammerstein Equations
AMS Subj. Classification: 47J10, 47H30, 47H10We study some possibilities of nonlinear spectral theories for solving nonlinear operator equations. The main aim is to research a spectrum and establish some kind of nonlinear Fredholm alternative for Hammerstein operator KF.
Note on spectral theory of nonlinear operators: Extensions of some surjectivity theorems of Fučík and Nečas
Notes on the Fučík spectrum and the mixed boundary value problem
The paper is devoted to the study of the properties of the Fučík spectrum. In the first part, we analyse the Fučík spectra of the problems with one second order ordinary differential equation with Dirichlet, Neumann and mixed boundary conditions and we present the explicit form of nontrivial solutions. Then, we discuss the problem with two second order differential equations with mixed boundary conditions. We show the relation between the Dirichlet boundary value problem and mixed boundary value...
On a Superlinear Elliptic Boundary Value Problem.
On nonlinear eigenvaule problems.
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory.
On the discreteness of the spectra of the Dirichlet and Neumann -biharmonic problems.