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, MartaManásevich, RaúlZanolin, Fabio Keywords: Quasilinear; p-Laplacian; Multiplicity; Fučík Spectrum Issue Date: 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 Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics43 (2011) Abstract: For $\varnothing$ an increasing homeomorphism from $\mathbb{R}$onto $\mathbb{R}$ and $f\epsilon C\left(\mathbb{R}\right)$, we considerthe 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 generalizedPseudo Fu$\check{\textrm{c}}$ik spectrum (at infinity, or at zero).New insights that lead to a very precise counting of solutions areobtained by splitting these spectra into two parts, called PositivePseudo Fu$\check{\textrm{c}}$ik Spectrum (PPFS) and Negative PseudoFu$\check{\textrm{c}}$ik spectrum (NPFS) (at infinity, or at zero,respectively), in this form tue can discuss separately the two casesu' (0) > 0 and u' (0) < 0. Type: Article URI: http://hdl.handle.net/10077/5720 ISSN: 0049-4704 eISSN: 2464-8728 Appears in Collections: Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.43 (2011)

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