The effective action for string theory which takes into account non-minimal coupling of moduli admits multi-black hole solutions. The euclidean continuation of these solutions can be interpreted as an instanton mediating the splitting and recombination of the throat of extremal magnetically charged black holes.

We present and analyze exact solutions of the Einstein–Maxwell and Einstein–Maxwell– Dilaton equations that describe static pairs of oppositely charged extremal black holes, i.e., black diholes. The holes are suspended in equilibrium in an external magnetic field. We comment as well on the relation of these solutions to brane–antibrane configurations in string and M-theory.

In this paper we use the method of upper and lower solutions to study multivalued Sturm{Liouville and periodic boundary value problems , with Caratheodory orientor eld. We prove two existence theorems. One when the orientor eld F (t; x; y) is convex{valued and the other when F (t; x; y) is nonconvex valued. Finally we show that the \convex" problem has extremal solutions in the order interval d...

for a bounded linear operator on hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎we study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎also we show that any quasinilpotent operator $t$ has an hypernoncyclic vector‎, ‎and so $t$ has a nontrivial hyperinvariant subspace‎.

We study the extremal solution for the problem (−∆)u = λf(u) in Ω, u ≡ 0 in R \ Ω, where λ > 0 is a parameter and s ∈ (0, 1). We extend some well known results for the extremal solution when the operator is the Laplacian to this nonlocal case. For general convex nonlinearities we prove that the extremal solution is bounded in dimensions n < 4s. We also show that, for exponential and power-like ...

We present a class of black p-brane solutions of M-theory which were hitherto known only in the extremal supersymmetric limit, and calculate their macroscopic entropy and temperature.

In this paper we prove existence results for extremal solutions of the first order discontinuous impulsive differential inclusions with periodic boundary conditions and impulses at the fixed times under certain monotonicity conditions of the multi-valued functions.

General properties of intersecting extremal p-brane solutions of gravity coupled with dilatons and several different d-form fields in arbitrary space-time dimensions are considered. It is shown that heuristically expected properties of the intersecting p-branes follow from the explicit formulae for solutions. In particular, harmonic superposition and S-duality hold for all p-brane solutions. Ge...

This paper investigates the existence of the extremal solutions to the integral boundary value problem for first-order impulsive functional integrodifferential equations with deviating arguments under the assumption of existing upper and lower solutions in the reversed order. The sufficient conditions for the existence of solutions were obtained by establishing several new comparison principles...

We provide regularity results at the boundary for continuous viscosity solutions to nonconvex fully nonlinear uniformly elliptic equations and inequalities in Euclidian domains. We show that (i) any solution of two sided inequalities with Pucci extremal operators is C1,α on the boundary; (ii) the solution of the Dirichlet problem for fully nonlinear uniformly elliptic equations is C2,α on the b...