A Schechter type critical point result in annular conical domains of a Banach space and applications
Year: 2016
Type: article
Abstract: Using Ekeland's variational principle we obtain a critical point theorem ofSchechter type for extrema of a functional in an annular conical domain of aBanach space. The result can be seen as a variational analogue ofKrasnoselskii's fixed point theorem in cones and can be applied for theexistence, localization and multiplicity of the positive solutions ofvariational problems. The result is then applied to $p$-Laplace equations,where the geometric condition on the boundary of the annular conical domainis established via a weak Harnack type inequality given in terms of theenergetic norm. This method can be applied also to other homogeneousoperators in order to obtain existence, multiplicity or infinitely manysolutions for certain classes of quasilinear equations.
Authors: Hannelore Lisei, Radu Precup, Csaba Varga
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2323882810