TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS

TABLE OF CONTENTS

Title and Author(s)		Page
	Topological Characteristic of Fully Nonlinear Parabolic Boundary Value Problems Igor V. Skrypnik and Igor B. Romanenko ABSTRACT. A general nonlinear initial boundary value problem is being considered, where is a bounded open set in Rn with sufficiently smooth boundary. The problem (1)-(3) is then reduced to an operator equation Au = 0, where the operator A satisfies (S)+ condition. The local and global solvability of the problem (1)-(3) are achieved via topological methods developed by the first author. Further applications involving the convergence of Galerkin approximations are also given.	1
	On the Neumann Problem Involving the Critical Sobolev Exponent Jan Chabrowski and Pedro Girao ABSTRACT. In this paper we consider the exterior Neumann problem (P) involving the critical Sobolew exponent. We investigate two cases where the coefficient a interferes or not with the spectrum of the Lapalce operator with the Neumann boundary conditions. In both cases we establish the existence of solutions.	33
	Compact Components of Positive Solutions for Superlinear Indefinite Elliptic Problems of Mixed Type Santiago Cano-Casanova ABSTRACT. In this paper we construct an example of superlinear indefinite weighted elliptic mixed boundary value problem exhibiting a mushroom shaped compact component of positive solutions emanating from the trivial solution curve at two simple eigenvalues of a related linear weighted boundary value problem. To perform such construction we have to adapt to our general setting some of the rescaling arguments of H. Amann and J. Lopez-Gomez [2, Section 4] to get a priori bounds for the positive solutions. Then, using the theory of [1], [4] and [5], we give some sufficient conditions on the nonlinearity and the several potentials of our model setting so that the set of values of the parameter for which the problem possesses a positive solution is bounded. Finally, the existence of the component of positive solutions emanating from the trivial curve follows from the unilateral results of P. H. Rabinowitz ([18], [14]). Monotonicity methods, re-scaling arguments, Liouville type theorems, local bifurcation and global continuation are among the main technical tools used to carry out our analysis.	45
	Existence and Multiplicity Results for Wave Equations with Time-Independent Nonlinearity Christian Fabry and Patrick Habets ABSTRACT. We study 2-periodic solutions of u'' + f(t,u) = 0 using positively homogeneous asymptotic approximations of this equation near zero and infinity. Our main results concern the degree of I - P, where P is the Poincare map associated to these approximations. We indicate classes of problems, some with degree 1 and others with degree different from 1. Considering results based on first order approximations, we work out examples of equations for which the degree is the negative of any integer.	73
	Multiple Periodic Solutions of Asymptotically Linear Hamiltonian Systems via Conley Index Theory Guihua Fei ABSTRACT. In this paper we study the existence of periodic solutions of asymptotically linear Hamiltonian systems which may not satisfy the Palais-Smale condition. By using the Conley index theory and the Galerkin approximation methods, we establish the existence of at least two nontrivial periodic solutions for the corresponding systems.	89
	Differential Inclusions on Closed Set in Banach spaces with Application to Sweeping Process Houcine Benabdellah ABSTRACT. This paper deals with the existence of absolutely continuous solutions of a differential inclusion with state constraint in a separable Banach space where C: [0,a] X is a multifunction with closed graph G and F: G X is a convex compact valued multifunction which is separately measurable in t [0,a] and separately upper semicontinuous in x X. Application to a non convex sweeping process is also considered.	115
	Aroszajn Type Results for Volterra Equations and Inclusions Ravi P. Agarwal, Lech Górniewicz and Donal O'Regan ABSTRACT. This paper discusses the topological structure of the set of solutions for a variety of Volterra equations and inclusions. Our results rely on the existence of a maximal solution for an appropriate ordinary differential equation.	149
	Dimension and infinitesimal groups of Cantor minimal systems Jan Kwiatkowski and Marcin Wata ABSTRACT. The dimension and infinitesimal groups of a Cantor dynamical system (X,T) are inductive limits of sequences of homomorphisms defined by a proper Bratteli diagram of (X,T). A method of selecting sequences of homomorphisms determining the dimension and the infinitesimal groups of (X,T) based on non-proper Bratteli diagrams is described. The dimension and infinitesimal groups of Rudin-Shapiro, Morse and Chacon flows are computed.	161