Open AccessNodal solutions for (𝑝,2)-equations
Author(s) -
Sergiu Aizicovici,
Nikolaos S. Papageorgiou,
Vasile Staicu
Publication year - 2014
Publication title -
transactions of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.798
H-Index - 100
eISSN - 1088-6850
pISSN - 0002-9947
DOI - 10.1090/s0002-9947-2014-06324-1
Subject(s) - algorithm , computer science , annotation , artificial intelligence , mathematics , database
In this paper, we study a nonlinear elliptic equation driven by thesum of a p-Laplacian and a Laplacian ((p, 2)-equation), with a Carathéodory(p − 1)-(sub-)linear reaction. Using variational methods combined with Morsetheory, we prove two multiplicity theorems providing precise sign informationfor all the solutions (constant sign and nodal solutions). In the process, weprove two auxiliary results of independent interest