Existence and multiplicity of solutions for a class of forced vibration problems with obstacles Original Research Article

By variational methods, an existence theorem and two multiplicity theorems of solutions of the following forced vibration problems are obtained: equation(1.1) View the MathML source−ẍ=q(x)|ẋ|2+g(t)ẋ+f(t) Turn MathJax on with equation(1.2) View the MathML sourcex(0)−x(2π)=ẋ(0)−ẋ(2π)=0,x(t)≥0,∀t∈R Turn MathJax on and equation(1.3) View the MathML sourceẋ(t0−)=−ẋ(t0+),ifx(t0)=0, Turn MathJax on where