Energy-based localization of positive solutions for stationary Kirchhoff type equations and systems

Institutul de Studii Avansate în Ştiinţă şi Tehnologie – Institutul STAR-UBB Centrul de cercetare Analiză Aplicată organizează Seminarul de Operatori Neliniari și Ecuații Diferențiale, Joi 17 noiembrie ora 10:30, sala “e”, clădirea “Mathematica”, strada Ploiesti nr. 23 susținută de către Dr. Nataliia Kolun Military Academy, Odessa, Ukraine.

We are concerned with positive solutions for the Dirichlet boundary value problem for equations and systems of Kirchhoff type. We obtain existence and localization results of positive solutions using Krasnosel’skiˇı’s fixed point theorem in cones and a weak Harnack type inequality. The localization is given in terms of energy norm, being of interest from a physical point of view. In the case of systems, the results on the localization are established componentwise using the vector version of Krasnosel’skiˇı’s theorem, which allows some of the equations of the system to satisfy the compression condition and others the expansion one.