Title: TBA
Abstract: TBA

Title: Infinitely many entire solutions to the curl-curl problem with critical exponent
Abstract: We prove the existence of an unbounded sequence of solutions to the curl-curl problem with critical exponent via a variational approach and suitable group actions to recover compactness.

Title: Superdiffusive Fractional In time NLS: Nonlinear Theory
Abstract: We consider a new class of partial differential equations dubbed Superdiffusive Fractional-In-Time Nonlinear Schrödinger equations on bounded domains. This equation will serve as a proper interpolation between the nonlinear Schrödinger equation and the Klein-Gordon Wave equation by making use of the (nonlocal in time) Caputo fractional time derivative of order $1<\beta< 2$. In space, we consider nonnegative $L^2(X)$ self-adjoint operators $A$ which include Laplacians and the (nonlocal in space) fractional Laplace operators with appropriate boundary conditions. In this talk, we present recent advances in the nonlinear theory, behavior of solutions, and potential applications as a control problem. Such models will serve appropriately in the important study of nonlinear optics through dispersive media and in the study of Bose-Einstein condensates.