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Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/5720

Title: Splitting the Fučík Spectrum and the Number of Solutions to a Quasilinear ODE
Authors: García-Huidobro, Marta
Manásevich, Raúl
Zanolin, Fabio
Keywords: Quasilinear
p-Laplacian
Multiplicity
Fučík Spectrum
Issue Date: 2011
Publisher: EUT Edizioni Università di Trieste
Citation: 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
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
43 (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.
URI: http://hdl.handle.net/10077/5720
ISSN: 0049-4704
MS Classification 2000: 34B15
34A34
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