175 research outputs found
Existence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems
We prove the existence of positive periodic solutions for the second order
nonlinear equation , where has superlinear growth at
zero and at infinity. The weight function is allowed to change its sign.
Necessary and sufficient conditions for the existence of nontrivial solutions
are obtained. The proof is based on Mawhin's coincidence degree and applies
also to Neumann boundary conditions. Applications are given to the search of
positive solutions for a nonlinear PDE in annular domains and for a periodic
problem associated to a non-Hamiltonian equation.Comment: 41 page
Chaotic dynamics in the Volterra predator-prey model via linked twist maps
We prove the existence of infinitely many periodic solutions and complicated
dynamics, due to the presence of a topological horseshoe, for the classical
Volterra predator--prey model with a periodic harvesting. The proof relies on
some recent results about chaotic planar maps combined with the study of
geometric features which are typical of linked twist maps.Comment: 24 pages, 4 figure
Multiple positive solutions for a superlinear problem: a topological approach
We study the multiplicity of positive solutions for a two-point boundary
value problem associated to the nonlinear second order equation .
We allow to change its sign in order to cover the case of
scalar equations with indefinite weight. Roughly speaking, our main assumptions
require that is below as and above
as . In particular, we can deal with the situation
in which has a superlinear growth at zero and at infinity. We propose
a new approach based on the topological degree which provides the multiplicity
of solutions. Applications are given for , where we prove
the existence of positive solutions when has positive
humps and is sufficiently large.Comment: 36 pages, 3 PNG figure
Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case
We study the periodic and the Neumann boundary value problems associated with
the second order nonlinear differential equation \begin{equation*} u'' + c u' +
\lambda a(t) g(u) = 0, \end{equation*} where is a
sublinear function at infinity having superlinear growth at zero. We prove the
existence of two positive solutions when and
is sufficiently large. Our approach is based on Mawhin's
coincidence degree theory and index computations.Comment: 26 page
Remarks on Dirichlet problems with sub linear growth at infinity
We present some existence and multiplicity results for positive solutions to the Dirichlet problem associated with; under suitable conditions on the nonlinearity g(u)and thew eight function a(x): The assumptions considered are related to classical theorems about positive solutions to a sublinear elliptic equation due to Brezis-Oswald and Brown-Hess
Some Remarks on Fixed Points for Maps which are Expansive along one Direction
We present some fixed point theorems for planar maps
which satisfy a property of path–expansion along a certain direction.
We also show some links between these fixed point theorems
and other recent results about covering relations and topological
horseshoes
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