TY - JOUR
T1 - A local minimum theorem and critical nonlinearities
AU - Bonanno, Gabriele
AU - D’Aguì, Giuseppina
AU - O’Regan, Donal
N1 - Publisher Copyright:
© 2016, Ovidius University. All rights reserved.
PY - 2016
Y1 - 2016
N2 - In this paper the existence of two positive solutions for a Dirichlet problem having a critical growth, and depending on a real parameter, is established. The approach is based on methods which are totally variational, unlike the fundamental result of Ambrosetti, Brezis and Cerami where a clever combination of topological and variational methods is used in order to obtain the same conclusion. In addition, a numerical estimate of real parameters, for which the two solutions are obtained, is provided. Our main tool is a local minimum theorem.
AB - In this paper the existence of two positive solutions for a Dirichlet problem having a critical growth, and depending on a real parameter, is established. The approach is based on methods which are totally variational, unlike the fundamental result of Ambrosetti, Brezis and Cerami where a clever combination of topological and variational methods is used in order to obtain the same conclusion. In addition, a numerical estimate of real parameters, for which the two solutions are obtained, is provided. Our main tool is a local minimum theorem.
KW - Critical growth
KW - Local minimum
KW - Nonlinear differential problem
KW - Palais-smale condition
KW - Variational methods
UR - https://www.scopus.com/pages/publications/84991721738
U2 - 10.1515/auom-2016-0028
DO - 10.1515/auom-2016-0028
M3 - Article
SN - 1224-1784
VL - 24
SP - 67
EP - 86
JO - Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
JF - Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
IS - 2
ER -