Towards Solutions of Seepage Problems

Existence of multiple solutions for Sturm-Liouville boundary value problems

In this paper, based on variational methods and critical point theory, we guarantee the existence of infinitely many classical solutions for a two-point boundary value problem with fourth-order Sturm-Liouville equation; Some recent results are improved and by presenting one example, we ensure the applicability of our results.

A strong convergence theorem for solutions of zero point problems and fixed point problems

Zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎A strong convergence theorem for the common solutions of the problems is established in the framework of Hilbert spaces‎.

Common solutions to pseudomonotone equilibrium problems

‎In this paper‎, ‎we propose two iterative methods for finding a common solution of a finite family of equilibrium problems ‎for pseudomonotone bifunctions‎. ‎The first is a parallel hybrid extragradient-cutting algorithm which is extended from the‎ ‎previously known one for variational inequalities to equilibrium problems‎. ‎The second is a new cyclic hybrid‎ ‎extragradient-cutting algorithm‎....

Solutions to homework problems

1 Homework Assignment # 1 1. Show that the -δ definition of continuity of a map f : X → Y between metric spaces is equivalent to the definition of continuity in terms of open subsets. Proof. Suppose f is -δ-continuous (i.e., continuous in the sense of the -δ definition of continuity) and that U is an open subset of Y . We need to show that f−1(U) is an open subset of X. The definition of an ope...

Creative Solutions to Problems