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

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.