121 research outputs found
Qualitative properties and existence of sign changing solutions with compact support for an equation with a p-Laplace operator
We consider radial solutions of an elliptic equation involving the p-Laplace
operator and prove by a shooting method the existence of compactly supported
solutions with any prescribed number of nodes. The method is based on a change
of variables in the phase plane corresponding to an asymptotic Hamiltonian
system and provides qualitative properties of the solutions
Highly oscillatory solutions of a Neumann problem for a -laplacian equation
We deal with a boundary value problem of the form where for and , and is a
double-well potential. We study the limit profile of solutions when and, conversely, we prove the existence of nodal solutions associated
with any admissible limit profile when is small enough
Splitting the Fučík Spectrum and the Number of Solutions to a Quasilinear ODE
For an increasing homeomorphism from
onto and , we consider
the problem
The aim is to study multiplicity of solutions by means of some generalized
Pseudo Fuik spectrum (at infinity, or at zero).
New insights that lead to a very precise counting of solutions are
obtained by splitting these spectra into two parts, called Positive
Pseudo Fuik Spectrum (PPFS) and Negative Pseudo
Fuik spectrum (NPFS) (at infinity, or at zero,
respectively), in this form tue can discuss separately the two cases
u' (0) > 0 and u' (0) < 0
Existence of positive solutions of a superlinear boundary value problem with indefinite weight
We deal with the existence of positive solutions for a two-point boundary
value problem associated with the nonlinear second order equation
. The weight is allowed to change its sign. We assume
that the function is
continuous, and satisfies suitable growth conditions, so as the case
, with , is covered. In particular we suppose that is
large near infinity, but we do not require that is non-negative in a
neighborhood of zero. Using a topological approach based on the Leray-Schauder
degree we obtain a result of existence of at least a positive solution that
improves previous existence theorems.Comment: 12 pages, 4 PNG figure
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