Positive solutions of boundary value problems with p-Laplacian

In this article, we study a class of boundary value problems with p-Laplacian. By using a "Green-like" functional and applying the fixed point index theory, we obtain eigenvalue criteria for the existence of positive solutions. Several explicit conditions are derived as consequences, and further results are established for the multiplicity and nonexistence of positive solutions. Extensions are also given to partial differential BVPs with p-Laplacian defined on annular domains.