Existence and qualitative properties of solutions for nonlinear Dirichlet problems | Zendy

Alfonso Castro | Zendy; Jorge Cossío | Zendy; Carlos Vélez | Zendy

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Existence and qualitative properties of solutions for nonlinear Dirichlet problems

Author(s) -

Alfonso Castro,

Jorge Cossío,

Carlos Vélez

Publication year - 2012

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2013.33.123

Subject(s) - saddle point , sign (mathematics) , mathematics , morse code , nonlinear system , a priori and a posteriori , saddle , dirichlet distribution , degree (music) , mathematical analysis , pure mathematics , mathematical optimization , computer science , physics , geometry , boundary value problem , telecommunications , philosophy , epistemology , quantum mechanics , acoustics

sign-changing solutions to semilinear elliptic problems in connection with their Morse indices. To this end, we first establish a priori bounds for one-sign solutions. Secondly, using abstract saddle point principles we find large augmented Morse index solutions. In this part, extensive use is made of critical groups, Morse index arguments, Lyapunov-Schmidt reduction, and Leray-Schauder degree. Finally, we provide conditions under which these solutions necessarily change sign and we comment about further qualitative properties.

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