@article{Xia2022, 
author = {Minggang Xia and Xingyong Zhang and Danyang Kang and Cuiling Liu},
title = {Existence and concentration of nontrivial solutions for an elastic beam equation with local nonlinearity},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {1},
pages = {579-605},
keywords = {weak solution, elastic beam equation, local nonlinearity, mountain pass theorem, concentration},
url = {https://www.sciopen.com/article/10.3934/math.2022037},
doi = {10.3934/math.2022037},
abstract = {In this paper, by using the mountain pass lemma and the skill of truncation function, we investigate the existence and concentration phenomenon of nontrivial weak solutions for a class of elastic beam differential equation with two parameters    λ and    μ when the nonlinear term satisfies some growth conditions only near the origin. In particular, we obtain a concrete lower bound of the parameter    λ, and analyze the relationship between    λ and    μ. In the end, we investigate the concentration phenomenon of solutions when    μ  →  0, and obtain a specific lower bound of the parameter    λ which is independent of    μ.}
}