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AMJCUB
Applied Mathematics-A Journal of Chinese Universities  2018, Vol. 33 Issue (1): 71-87    DOI: 10.1007/s11766-018-3449-4
    
Existence and uniqueness results for mild solutions of random impulsive abstract neutral partial differential equation over real axis
P Indhumathi1, A Leelamani2
1 Department of Mathematics, Tamilnadu College of Engineering, Coimbatore-641 659, Tamil Nadu, India. Email: drindhumathsj14@gmail.com
2 Department of Mathematics, Anna University Regional Centre, Coimbatore-641 046, Tamil Nadu, India. Email: aleelamani@gmail.com
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Abstract  In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle. Finally an example is given to illustrate our problem.

Key words： neutral equation      Leray Schauder Alternative      Banach Contraction Principle      semigroup of linear operators     
Received: 16 June 2016      Published: 28 March 2018
CLC:  34K40  
  34A37  
  35A01  
  35A02  
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P Indhumathi, A Leelamani. Existence and uniqueness results for mild solutions of random impulsive abstract neutral partial differential equation over real axis. Applied Mathematics-A Journal of Chinese Universities, 2018, 33(1): 71-87.

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http://www.zjujournals.com/amjcub/10.1007/s11766-018-3449-4     OR     http://www.zjujournals.com/amjcub/Y2018/V33/I1/71


Existence and uniqueness results for mild solutions of random impulsive abstract neutral partial differential equation over real axis

In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle. Finally an example is given to illustrate our problem.

关键词： neutral equation,  Leray Schauder Alternative,  Banach Contraction Principle,  semigroup of linear operators 
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