A LOCAL EXISTENCE THEOREM FOR A CLASS OF DELAY DIFFERENTIAL EQUATIONS

作者：Vrabie Joan I^*

来源：Topological Methods in Nonlinear Analysis, 2016, 48(2): 597-612.

DOI：10.12775/TMNA.2016.023

• Delay differential equations
• local existence
• metric fixed point arguments
• topological fixed point arguments
• semilinear wave equation
• pseudoparabolic equation

The goal of this paper is to show that some classes of partial differential functional equations admit a natural formulation as ordinary functional differential equations in infinite dimensional Banach spaces. Moreover, the equations thus obtained are driven by continuous right-hand sides satisfying the compactness assumptions required by the infinite-dimensional version of a Peano-like existence theorem. Two applications, one to a semi-linear wave equation with delay and another one to a pseudoparabolic PDE in Mechanics, are included.

• 出版日期2016-12