Existence and multiplicity results for some nonlinear problems with singular ϕ -Laplacian via a geometric approach

Boundary value problems

Qihuai Liu¹  Xuelei Wang²  Dingbian Qian³ 

[1] School of Information and Technology, Shandong Agricultural University, Taian, China;School of Mathematical Sciences, Soochow University, Suzhou, China;School of Mathematics and Computing Sciences, Guilin University of Electronic Technology, Guilin, China

关键词: periodic solution;    geometric approach;    relativistic oscillator;    singular ϕ-Laplacian;   

DOI  :  10.1186/s13661-016-0554-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

New results on the existence and multiplicity of the solutions for some nonlinear boundary value problems with singular ϕ-Laplacian are obtained via a bend-twist fixed point theorem. These results improve related theorems in the previous literature. Moreover, the geometric approach in this paper provides a new method to investigate the existence and multiplicity of periodic motions of charged particles in a three-dimensional electromagnetic field.

【 授权许可】

CC BY