Abstract We study a double phase Neumann problem with superlinear reaction which need not satisfy the Ambrosetti-Rabinowitz condition. Using Nehari manifold method, we show that has at least three nontrivial bounded ground state solutions, all sign information (positive, negative and nodal).

In this paper, we study greedy variants of quasi-Newton methods. They are based on the updating formulas from a certain subclass Broyden family. particular, includes well-known DFP, BFGS, and SR1 updates. However, in contrast to classical methods, which use difference successive iterates for Hessian approximations, our methods apply basis vectors, greedily selected so as maximize measure progre...