Existence of positive solutions for second-order differential equations with two-point boundary value problems involving p-Laplacian

In this paper, we study a two-point boundary value problem involving p-Laplacian and its relationship with the associated discrete ones. Specifically, by using discrete variational methods, we first obtain a sequence of positive solutions for the associated discrete two-point boundary value problems corresponding to different step lengths. Then, utilizing the sequence of positive solutions, we construct a sequence of continuous functions which can be shown to be precompact. Finally, we prove that the limit function of the convergent subsequence is the desired positive solution. In particular, our result covers the cases when the nonlinear function in the equation is \((p-1)\) $(p-1)$ -superlinear and asymptotically \((p-1)\) $(p-1)$ -linear.