Discrete and Continuous Dynamical Systems - S
May 2021 , Volume 14 , Issue 5
Issue on applications of mathematical analysis to problems in theoretical physics
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We perform a semiclassical analysis for the planar Schrödinger-Poisson system
There are many natural phenomena that can best be described by the use of infinitesimal and infinite numbers (see e.g. [
We give short survey on the question of asymptotic stability of ground states of nonlinear Schrödinger equations, focusing primarily on the so called nonlinear Fermi Golden Rule.
After reviewing the theory of "causal fermion systems" (CFS theory) and the "Events, Trees, and Histories Approach" to quantum theory (ETH approach), we compare some of the mathematical structures underlying these two general frameworks and discuss similarities and differences. For causal fermion systems, we introduce future algebras based on causal relations inherent to a causal fermion system. These algebras are analogous to the algebras previously introduced in the ETH approach. We then show that the spacetime points of a causal fermion system have properties similar to those of "events", as defined in the ETH approach. Our discussion is underpinned by a survey of results on causal fermion systems describing Minkowski space that show that an operator representing a spacetime point commutes with the algebra in its causal future, up to tiny corrections that depend on a regularization length.
We prove the existence of positive solutions for a class of semipositone problems with singular Trudinger-Moser nonlinearities. The proof is based on compactness and regularity arguments.
We consider quasilinear elliptic equations, including the following Modified Nonlinear Schrödinger Equation as a special example:
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