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Splitting the Fučík Spectrum and the Number of Solutions to a Quasilinear ODE
García-Huidobro, Marta
Manásevich, Raúl
Zanolin, Fabio
2011
Abstract
For $\varnothing$ an increasing homeomorphism from $\mathbb{R}$
onto $\mathbb{R}$ and $f\epsilon C\left(\mathbb{R}\right)$, we consider
the problem
\[
\left(\varnothing\left(u'\right)\right)'+f\left(u\right)=0,\qquad t\epsilon\left(0,L\right),\qquad u\left(0\right)=0=u\left(L\right).
\]
The aim is to study multiplicity of solutions by means of some generalized
Pseudo Fu$\check{\textrm{c}}$ik 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 Fu$\check{\textrm{c}}$ik Spectrum (PPFS) and Negative Pseudo
Fu$\check{\textrm{c}}$ik 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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
43 (2011)
Publisher
EUT Edizioni Università di Trieste
Source
M. García-Huidobro, R. Manásevich and F. Zanolin, "Splitting the Fučík Spectrum and the Number of Solutions to a Quasilinear ODE", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 43 (2011), pp. 111–145
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it
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