Utilizing the theory of fixed point index for compact maps, we establish new results on the existence of positive solutions for a certain third order boundary value problem. The boundary conditions that we study are of nonlocal type, involve Stieltjes integrals and are allowed to be nonlinear.
We provide a theoretical study of the iterative hard thresholding with partially known support set (IHT-PKS) algorithm when used to solve the compressed sensing recovery problem. Recent work has shown that IHT-PKS performs better than the traditional IHT in reconstructing sparse or compressible signals. However, less work has been done on analyzing the performance guarantees of IHT-PKS. In this paper, we improve the current RIP-based bound of IHT-PKS algorithm from to , where is the restricted...
We consider the singular boundary value problem where is a given continuous function defined on the set which can have a time singularity at and a space singularity at . Moreover, , , and , , are real constants such that , whereas . The main aim of this paper is to discuss the existence of solutions to the above problem and apply the general results to cover certain classes of singular problems arising in the theory of shallow membrane caps, where we are especially interested in...