in this paper, a vector version of the intermediate value theorem is established. the main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{on fixed point theorems for monotone increasing vector valued mappings via scalarizing}, positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

We get a uniqueness theorem for a Robin type boundary value problem for the Laplace equation arising in Physical Geodesy in the context of the gravimetric determination of the geoid. The boundary is an oblate ellipsoid of revolution and we have uniqueness of solutions provided that its eccentricity is (approximately) less than 0.526428.

By constructing a special cone and applying the fixed index theory in the cone, we prove the existence of positive solutions for a class of singular m-point boundary-value problems.

Sufficient conditions are given for the existence of multiple positive solutions of a boundary value problem of the form x′′(t)+q(t)f(x(t)) = 0, t ∈ [0, 1], x(0) = 0 and x(1) = R β α x(s)dg(s), where 0 < α < β < 1. A weaker boundary value problem is used to get information on the corresponding integral operator. Then the results follow by applying the Krasnosel’skĭı fixed point theorem on a sui...

In this manuscript, some tripled fixed point results were derived under (?,?,?)-contraction in the framework of ordered partially metric spaces. Moreover, we furnish an example which supports our theorem. Furthermore, about a homotopy are obtained. Finally, theoretical involved applications, such as finding unique solution to boundary value problems and theory.

The essence of the boundary-field equation method is the reduction of the boundary value problem under consideration to an equivalent nonlocal boundary value problem in a bounded domain by using boundary integral equations. The latter can then be treated by the standard variational method including its numerical approximations. In this paper, various formulations of the nonlocal boundary value ...