performance measure approach (pma) is a method for evaluating the probabilistic constraints in reliability-based design optimization of structures. the advanced mean-value (amv) method is suitable for pma, simply and efficiently. the iterative amv scheme could be yielded to unstable solutions such as periodic-oscillation and chaos for highly nonlinear performance functions. in the present paper...

This paper studies the existence of symmetric positive solutions for a second order nonlinear semipositone boundary value problem with integral boundary conditions by applying the Krasnoselskii fixed point theorem. Emphasis is put on the fact that the nonlinear term f may take negative value. An example is presented to demonstrate the application of our main result.

In this paper, we establish two fixed point theorems of Krasnoselskii type for the sum of A + B, where A is a compact operator and I − B may not be injective. Our results extend previous ones. As an application, we apply such results to obtain some existence results of periodic solutions for delay integral equations and then give three instructive examples.

Let [Formula: see text], [Formula: see text], and [Formula: see text] be a strongly monotone and Lipschitz mapping. A Krasnoselskii-type sequence is constructed and proved to converge strongly to the unique solution of [Formula: see text]. Furthermore, our technique of proo f is of independent interest.

‎This paper develops iterative method described by [V‎. ‎Daftardar-Gejji‎, ‎H‎. ‎Jafari‎, ‎An iterative method for solving nonlinear functional equations‎, ‎J‎. ‎Math‎. ‎Anal‎. ‎Appl‎. ‎316 (2006) 753-763] to solve Ito stochastic differential equations‎. ‎The convergence of the method for Ito stochastic differential equations is assessed‎. ‎To verify efficiency of method‎, ‎some examples are ex...