A remark on irrational equations

A Remark on Nonlinear Dirac Equations

For a n-dimensional spin manifold M with a fixed spin structure and a spinor bundle ΣM , we prove an -regularity theorem for weak solutions to the nonlinear Dirac equation of cubic nonlinearity. This, in particular, answers a regularity question raised by Chen-Jost-Wang [5] when n = 2.

A remark for dynamic equations on time scales

We give a proposal to generalize the concept of the differential equations on time scales [1, 2, 3], such that they can be more appropriate for the analysis of real world problems, and give more opportunities to increase the theoretical depth of investigation.

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Remark on the equations of axially symmetric gravitational fields

A local theorem of existence and uniqueness of solutions of the equations of stationary axially symmetric vacuum gravitational fields in the general theory of relativity close to the flat space solution is proved using the implicit function theorem in Banach spaces. Mathematics Subject Classification (2010). 83C10, 83C05

ONE REMARK ON BARELY Ḣp SUPERCRITICAL WAVE EQUATIONS

We prove that a good Ḣp critical theory for the 3D wave equation ∂ttu − △u = −|u|p−1u can be extended to prove global well-posedness of smooth solutions of at least one 3D barely Ḣp supercritical wave equation ∂ttu −△u = −|u|p−1ug(|u|), with g growing slowly to infinity, provided that a Kenig-Merle type condition is satisfied. This result extends those [26, 18] obtained for the particular case ...