RT - Journal Article
T1 - Existence of at least one nontrivial solution for a class of problems involving both p(x)-Laplacian and p(x)-Biharmonic
JF - khu-mmr
YR - 2022
JO - khu-mmr
VO - 8
IS - 1
UR - http://mmr.khu.ac.ir/article-1-3035-en.html
SP - 167
EP - 183
K1 - p(x)-biharmonic operator
K1 - p(x)-harmonic operator
K1 - Palais-Smale condition
K1 - Mountain Pass theorem
K1 - generalized Lebesgue-Sobolev space.
AB - We investigate the existence of a weak nontrivial solution for the following problem. Our analysis is generally bathed on discussions of variational based on the Mountain Pass theorem and some recent theories one the generalized Lebesgue-Sobolev space. This paper guarantees the existence of at least one weak nontrivial solution for our problem. More precisely, by applying Ambrosetti and Rabinowitz’s mountain pass theorem and under appropriate conditions, we show that there exists a positive number such that our problem has at least one nontrivial weak solution.
LA eng
UL http://mmr.khu.ac.ir/article-1-3035-en.html
M3
ER -