Abstract. We consider a nonlinear Dirichlet problem driven by a nonautonomous ()-differential operator and with a reaction having the competing effects of a parametric singular term and a ()-linear perturbation which can be resonant as with respect to the principal eigenvalue of the relevant operator. If the resonance is from the left, then we demonstrate that the problem has a positive solution for all values of the parameter and if the driving differential operator is only the nonautonomous -Laplacian, then the positive solution is unique. On the other hand, if the resonance is from the right, then we prove an existence and multiplicity theorem which is global with respect to the parameter (a bifurcation-type theorem). Also, we conduct a detailed study of the continuity properties of solution multifunction.
How to Cite this Article:
J. Han, Z. Liu, N.S. Papageorgiou, J.C. Yao, Nonhomogeneous, nonautonomous resonant singular equations, J. Nonlinear Var. Anal. 10 (2026), 111-137.
