New existence results on nonhomogeneous Sturm–Liouville type BVPs for higher-order $p$-Laplacian differential equations
A class of nonlinear boundary value problems for $p$-Laplacian differential equations is studied. Sufficient conditions for the existence of solutions are established. The nonlinearities are allowed to be superlinear. We do not apply the Green's functions of the relevant problem and the methods of obtaining a priori bounds for solutions are different from known ones. Examples that cannot be covered by known results are given to illustrate our theorems.