TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS

TABLE OF CONTENTS

Title and Author(s)		Page
	Resolvent convergence for Laplace operators on unbounded curved squeezed domains Maria C. Carbinatto and Krzysztof P. Rybakowski ABSTRACT. We establish a resolvent convergence result for the Laplace operator on certain classes of unbounded curved squeezed domains $\Omega_\eps$ as $\eps\to0$. As a consequence, we obtain Trotter-Kato-type convergence results for the corresponding family of $C^0$-semigroups. This extends previous results obtained by Antoci and Prizzi in \cite{\rfa{AP}} in the flat squeezing case.	233
	Study on a quadratic Hadamard type fractional integral equation on an unbounded interval JinRong Wang, Chun Zhu and Yong Zhou ABSTRACT. In this paper, a quadratic Hadamard type fractional integral equations on an unbounded interval is studied. By applying a technique of measure of noncompactness and Schauder fixed point theorem, existence and uniform local attractivity of solutions are presented after overcoming some difficulty from the Hadamard type singular kernel. Moreover, three new solutions sets who tend to zero at infinity are constructed to obtain local stability of solutions. Finally, two examples are made to illustrate our theory results.	257
	Multiple solutions to a Dirichlet eigenvalue problem with p-Laplacian Salvatore A. Marano, Dumitru Motreanu and Daniele Puglisi ABSTRACT. The existence of a greatest negative, a smallest positive, and a nodal weak solution to a homogeneous Dirichlet problem with $p$-Laplacian and reaction term depending on a positive parameter is investigated via variational as well as topological methods, besides truncation techniques.	277
	Generalized Sturm-Liouville boundary conditions for first order differential systems in the plane Alessandro Fonda and Maurizio Garrione ABSTRACT. We study asymptotically positively homogeneous first order systems in the plane, with boundary conditions which are positively homogeneous, as well. Defining a generalized concept of Fuèik spectrum which extends the usual one for the scalar second order equation, we prove existence and multiplicity of solutions. In this way, on one hand we extend to the plane some known results for scalar second order equations (with Dirichlet, Neumann or Sturm-Liouville boundary conditions), while, on the other hand, we investigate some other kinds of boundary value problems, where the boundary points are chosen on a polygonal line, or in a cone. Our proofs rely on the shooting method.	293
	Rotation numbers for planar attractors of equivariant homeomorphisms Begona Alarcón ABSTRACT. Given an integer $m>1$ we consider $\Z_m$-equivariant and orientation preserving homeomorphisms in $\R^2$ with an asymptotically stable fixed point at the origin. We present examples without periodic points and having some complicated dynamical features. The key is a preliminary construction of $\Z_m$-equivariant Denjoy maps of the circle.	327
	Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems Alexandre N. Carvalho, Eder R. Aragao-Costa, Pedro Marín-Rubio and Gabriela Planas ABSTRACT. We consider an autonomous dynamical system coming from a coupled system in cascade where the uncoupled part of the system satisfies that the solutions comes from $-\infty $ and goes to $\infty $ to equilibrium points, and where the coupled part generates asymptotically a gradient-like nonlinear semigroup. Then, the complete model is proved to be also gradient-like. The interest of this extension comes, for instance, in models where a continuum of equilibrium points holds, and for example a £ojasiewicz-Simon condition is satisfied. Indeed, we illustrate the usefulness of the theory with several examples.	345
	Controllability for systems governed by second-order differential inclusions with nonlocal conditions Tran Dinh Ke and Valeri Obukhovskii ABSTRACT. We study a controllability problem for a system governed by a semilinear second-order differential inclusion involving control perturbations and nonlocal conditions in a Hilbert space. By using the fixed point theory for condensing multimaps, the $(E_0,X_0)$-controllability result for the mentioned problem is proved under the assumption that the corresponding linear system is $(E_0,X_0)$-controllable.	377
	On parametric equilibrium problems Marcel Bogdan and József Kolumbán ABSTRACT. The goal of this article is to study a kind of stability property of a sequence of solutions to parametric equilibrium problems. The main result gives sufficient conditions for this purpose, in the presence of the topological pseudomonotonicity in the limit problem.	405
	Note on periodic solutions of relativistic pendulum type systems Kazuya Hata, Jiaquan Liu and Zhi-Qiang Wang ABSTRACT. We establish multiplicity results of periodic solutions for relativistic pendulum type systems of ordinary differential equations. We provide a different approach to the problems and answer some questions raised in \cite{6}, \cite{7} by Brezis and Mawhin recently.	417
	Two positive solutions for one-dimensional p-Laplacian with a singular weight Ryuji Kajikiya, Yong-Hoon Lee and Inbo Sim ABSTRACT. We investigate a bifurcation problem for one-dimensional $p$-Laplace equation with a singular weight under Dirichlet boundary condition. Using super-subsolution method and mountain pass lemma, we prove the existence of at least two positive solutions, at least one positive solution and no positive solution according to the range of a bifurcation parameter.	427
	Existence and nonexistence of positive periodic solutions to a differential inclusion Yuqiang Feng and Ping Tong ABSTRACT. In this paper, the existence and nonexistence of positive periodic solutions for a second-order differential inclusion are considered. Some existence and nonexistence results are established by the use of Bohnenblust-Karlin's fixed-point theorem for multivalued operators and Sobolev constant.	449
	Solvability of fractional differential equations with integral boundary conditions at resonance Yude Ji and Weihua Jiang ABSTRACT. By using the coincidence degree theory due to Mawhin and constructing suitable operators, some sufficient conditions for the existence of solution for a class of fractional differential equations with integral boundary conditions at resonance are established, which are complement of previously known results. The interesting point is that we shall deal with the case $\text{\rm dim}\,\text{\rm Ker}\,L=2$, which will cause some difficulties in constructing the projector $Q$. An example is given to illustrate our result.	461