The main objective of the paper is to state newly fixed point theorems for set-valued mappings in the framework of 0-complete partial metric spaces which speak about a location of a fixed point with respect to an initial value of the set-valued mapping by using some $C$-class functions. The results proved herein generalize, modify and unify some recent results of the existing literature. As an ...

Abstract This article proposes new strategies for solving two-point Fractional order Nonlinear Boundary Value Problems (FNBVPs) with Robin Conditions (RBCs). In the numerical schemes, a FNBVP is transformed into system of Initial (FIVPs) unknown (ICs). To approximate ICs in FIVPs, we develop nonlinear shooting methods based on Newton’s method and Halley’s using RBC at right end point. deal FIVP...

This paper deals with a two-point boundary value problem for pseudodifferential equations and systems of second order under conditions containing operators. The need to consider operators is caused by two reasons, first, such appear more often in applied problems, second, considering equations, it possible achieve the well-posedness Schwartz space S its dual space.First, we scalar equation symb...

For one-dimensional p-Laplacian with weights in Lγ : L 0, 1 ,R 1 ≤ γ ≤ ∞ balls, we are interested in the extremal values of the mth positive half-eigenvalues associated with Dirichlet, Neumann, and generalized periodic boundary conditions, respectively. It will be shown that the extremal value problems for half-eigenvalues are equivalent to those for eigenvalues, and all these extremal values a...

Immersing a physical system in a heat bath results in the fields acquiring different properties according to their statistics. E.g., finite-temperature bosonic fields obey periodic boundary conditions, while fermionic fields satisfy antiperiodic b.c.’s. Such a distinction can be seen also at the level of the Green’s functions. Depending on the field’s statistics, thermal propagators obey either...

The Cauchy problem for the 2D Boussinesq system with periodic boundary conditions is studied. The global existence and uniqueness of a solution with initial data (u(0), θ(0)) ∈ Φ(α) is established, where Φ(α) is the space of functions the kth Fourier coefficients of which decay at infinity as 1 |k|α , α > 2. It is proved that the solution becomes analytic at any positive time. Bibliography: 10 ...