Boundary value problems with singular \(\varphi\)-Laplacians (Q2233221)

In this short note, the author presents sufficient conditions for the existence of a solution to systems of differential equations with singular \(\phi\)-Laplacians and Dirichlet, Sturm-Liouville, periodic or anti-periodic boundary conditions. These conditions include and in some cases generalize results in the literature. The proofs are based on reducing the search of solutions to finding the initial values of an equivalent system being a zero of a mapping in \(\mathbb R^n\) corresponding to the considered boundary conditions. This approach was already used by the author in the scalar case.