Quasi-periodic solutions for p-Laplacian equations with jumping nonlinearity and unbounded potential terms

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In this paper, we are concerned with the boundedness of all the solutions for a kind of second order differential equations with p-Laplacian term (ϕₚ(x'))'+aϕₚ(x+)-bϕₚ(x-)+f(x)=e(t), where x+= (x,0), x- =(-x,0), ϕₚ(s)=|s|ᵖ⁻²s, p≥2, a and b are positive constants (a=b), and satisfy 1a¹/ᵖ+1b¹/ᵖ=2ω⁻¹,where ω∈ +, the perturbation f is unbounded, e(t)∈ C⁶ is is a smooth 2πₚ-periodic function on t, where πₚ=2π(p-1)¹/ᵖpπp.