A large family of solutions, representing, in general, spherically symmetric Type II fluid, is presented, which includes most of the known solutions to the Einstein field equations, such as, the monopolede Sitter-charged Vaidya ones. PACS numbers: 04.20Jb, 04.40.+c. ∗e-mail address: [email protected] 1 In 1951, Vaidya [1] found a solution that represents an imploding (exploding) null dust f...

It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyl’s construction is generalized here to arbitrary dimension D ≥ 4. The general solution of the D-dimensional vacuum Einstein equations that admits D− 2 orthogonal com...

Article history: Received 10 November 2010 Available online 14 April 2011 JEL classification: C78

We introduce a new iterative scheme for nding a common elementof the solutions set of a generalized mixed equilibrium problem and the xedpoints set of an innitely countable family of nonexpansive mappings in a Banachspace setting. Strong convergence theorems of the proposed iterative scheme arealso established by the generalized projection method. Our results generalize thecorresponding results...

‎by considering a degenerate $p(x)-$laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent sobolev space is presented‎. ‎multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding nehari manifold‎.

in this article, the modified exp-function method is used to construct many exact solutions to the nonlineargeneralized k(n,n) and bbm equations with variable coefficients. under different parameter conditions, explicitformulas for some new exact solutions are successfully obtained. the proposed solutions are found to beimportant for the explanation of some practical physical problems.

in this work, we successfully construct the new exact traveling wave solutions ofthe generalized sinh–gordon equation by new application of the homogeneousbalance method. the idea introduced in this paper can be applied to othernonlinear evolution equations.