@article{El Ahmadi2024, 
author = {Mahmoud El Ahmadi and Mohammed Barghouthe and Anass Lamaizi and Mohammed Berrajaa},
title = {Existence and multiplicity results for a kind of double phase problems with mixed boundary value conditions},
year = {2024},
journal = {Communications in Analysis and Mechanics},
volume = {16},
number = {3},
pages = {509-527},
keywords = {double phase problems, variational methods, critical point theory, Cerami condition},
url = {https://www.sciopen.com/article/10.3934/cam.2024024},
doi = {10.3934/cam.2024024},
abstract = {In this article, we study a double phase variable exponents problem with mixed boundary value conditions of the form   {D(u)+|u|p(x)−2u+b(x)|u|q(x)−2u=f(x,u)inΩ,u=0onΛ1,(|∇u|p(x)−2u+b(x)|∇u|q(x)−2u)⋅ν=g(x,u)onΛ2.First of all, using the mountain pass theorem, we establish that this problem admits at least one nontrivial weak solution without assuming the Ambrosetti–Rabinowitz condition. In addition, we give a result on the existence of an unbounded sequence of nontrivial weak solutions by employing the Fountain theorem with the Cerami condition.}
}