A four-point boundary problem for a fractionalp-Laplacian differential equation is studied. The existence of two positive solutions is established by means of the monotone iterative method. An example supporting the abstract result is given.

This paper investigates the optimality conditions and scalarization theorems for robust approximate solutions to semi-infinite vector equilibrium problems with data uncertainty in the constraints. Under suitable constraint qualifications, we establish a necessary optimality condition for robust approximate quasi-weakly efficient solutions using the Clarke subdifferential. Subsequently, we present a sufficient optimality condition for such solutions under the assumption of approximate generalized convexity. Finally, we formulate two scalarization theorems for robust approximate quasi-weakly efficient solutions by employing a cone-strongly monotonic function. The definitions and main conclusions of this paper are supported by specific examples.