93 research outputs found
A note on a superlinear indefinite Neumann problem with multiple positive solutions
AbstractWe prove the existence of three positive solutions for the Neumann problem associated to u″+a(t)uγ+1=0, assuming that a(t) has two positive humps and ∫0Ta−(t)dt is large enough. Actually, the result holds true for a more general class of superlinear nonlinearities
Scattering parabolic solutions for the spatial N-centre problem
For the -centre problem in the three dimensional space, where ,
and , we prove the existence of entire parabolic trajectories
having prescribed asymptotic directions. The proof relies on a variational
argument of min-max type. Morse index estimates and regularization techniques
are used in order to rule out the possible occurrence of collisions
A priori bounds and multiplicity of positive solutions for -Laplacian Neumann problems with sub-critical growth
Let and let be either a ball or an
annulus. We continue the analysis started in [Boscaggin, Colasuonno, Noris,
ESAIM Control Optim. Calc. Var. (2017)], concerning quasilinear Neumann
problems of the type -\Delta_p u = f(u), \quad u>0 \mbox{ in } \Omega, \quad
\partial_\nu u = 0 \mbox{ on } \partial\Omega. We suppose that
and that is negative between the two zeros and positive after. In case
is a ball, we also require that grows less than the
Sobolev-critical power at infinity. We prove a priori bounds of radial
solutions, focusing in particular on solutions which start above 1. As an
application, we use the shooting technique to get existence, multiplicity and
oscillatory behavior (around 1) of non-constant radial solutions.Comment: 26 pages, 3 figure
Asymptotic and chaotic solutions of a singularly perturbed Nagumo-type equation
We deal with the singularly perturbed Nagumo-type equation where is a real parameter and is a piecewise constant function satisfying for all . We prove the existence of chaotic, homoclinic and
heteroclinic solutions, when is small enough. We use a dynamical
systems approach, based on the Stretching Along Paths method and on the
Conley-Wazewski's method
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
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