TY - JOUR
T1 - Existence of strong solutions of a p (x) -Laplacian Dirichlet problem without the Ambrosetti-Rabinowitz condition Dedicated to Prof. Xianling Fan on his 70th birthday
AU - Zhang, Qihu
AU - Zhao, Chunshan
N1 - Publisher Copyright:
© 2014 Elsevier Ltd.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - In this paper, we consider the existence of strong solutions of the following p(x)-Laplacian Dirichlet problem via critical point theory: -div( up(x)-2u)=f(x,u), in Ω,u=0, on Ω. We give a new growth condition, under which, we use a new method to check the Cerami compactness condition. Hence, we prove the existence of strong solutions of the problem as above without the growth condition of the well-known Ambrosetti-Rabinowitz type and also give some results about multiplicity of the solutions.
AB - In this paper, we consider the existence of strong solutions of the following p(x)-Laplacian Dirichlet problem via critical point theory: -div( up(x)-2u)=f(x,u), in Ω,u=0, on Ω. We give a new growth condition, under which, we use a new method to check the Cerami compactness condition. Hence, we prove the existence of strong solutions of the problem as above without the growth condition of the well-known Ambrosetti-Rabinowitz type and also give some results about multiplicity of the solutions.
KW - Ambrosetti-Rabinowitz condition
KW - Critical point
KW - Dirichlet problem
KW - Variable exponent space
KW - Without
KW - p (x) -Laplacian
UR - http://www.scopus.com/inward/record.url?scp=84919649072&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2014.10.022
DO - 10.1016/j.camwa.2014.10.022
M3 - Article
SN - 0898-1221
VL - 69
SP - 1
EP - 12
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 1
ER -