Premium
Existence of ground state solutions for Kirchhoff‐type problems involving critical Sobolev exponents
Author(s) -
Fan Haining
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4620
Subject(s) - mathematics , sobolev space , ground state , nehari manifold , critical exponent , type (biology) , compact space , exponent , manifold (fluid mechanics) , mathematical analysis , state (computer science) , pure mathematics , nonlinear system , geometry , physics , quantum mechanics , scaling , mechanical engineering , ecology , linguistics , philosophy , algorithm , engineering , biology
In this paper, we study the existence of ground state solutions for a Kirchhoff‐type problem in R 3 involving critical Sobolev exponent. With the help of Nehari manifold and the concentration‐compactness principle, we prove that problem admits at least one ground state solution.