In this paper, we prove an existence theorem for hyperbolic differential equations in Banach algebras under Lipschitz and Carathéodory conditions. The existence of extremal solutions is also proved under certain monotonicity conditions.

We present the main features of the physics of extremal black holes embedded in supersymmetric theories of gravitation, with a detailed analysis of the attractor mechanism for BPS and non-BPS black-hole solutions in four dimensions.

In this paper, we prove the existence of extremal positive, concave and pseudo-symmetric solutions for a general three-point second order p−Laplacian integro-differential boundary value problem by using an abstract monotone iterative technique.

The aim of this paper is to systematically present an area of extremal problems under dimension constraints. We state conjectures and solutions for many of these problems. Proofs will be given in several papers, each devoted to a specific problem.

*Correspondence: [email protected] Department of Information Engineering, China University of Geosciences Great Wall College, Baoding, Hebei 071000, P.R. China Abstract In this paper, we use monotone iterative technique in the presence of (coupled) upper and lower solutions in the reversed order to discuss the existence of extremal solutions (quasi-solutions) for causal differential equations wit...

In this paper, we deal with a coupled system of nonlinear fractional differential equations, which involve the Riemann-Liouville derivatives of different fractional orders. By using the monotone iterative technique combined with the method of upper and lower solutions, we not only obtain the existence of extremal system of solutions, but also establish iterative sequences for approximating the ...

We consider the stationary solutions of N = 4 supergravity coupled to n vector multiplets that define linear superpositions of non-interacting extremal black holes. The most general solutions of this type are derived from the graded decompositions of so(8, 2 + n) associated to its nilpotent orbits. We illustrate the formalism by giving explicitly asymptotically Minkowski non-BPS solutions of th...

In a multidimensional model with several scalar fields and an m -form we deal with classical spherically symmetric solutions with one (electric or magnetic) p -brane and Ricci-flat internal spaces and the corresponding solutions to the Wheeler–DeWitt (WDW) equation. Classical black holes are considered and their quantum analogues (e.g. for M2 and M5 extremal solutions in D = 11 supergravity, el...

The monotone iterative method is used to obtain sufficient conditions which guarantee that a delay differential equation with a nonlinear boundary condition has quasisolutions, extremal solutions, or a unique solution. Such results are obtained using techniques of weakly coupled lower and upper solutions or lower and upper solutions. Corresponding results are also obtained for such problems wit...

We present two diierent families of stationary black strings in three dimensions carrying electric and axion charges. Both solutions contain a singular region, which however is quite harmless for string frame geodesic observers, because the solutions are causally geodesically complete. In addition, we exhibit a variety of extremal limits of our solutions, and argue that there must exist a more ...