Mild solution of stochastic partial differential equation with nonlocal conditions and noncompact semigroups
-
Xuping Zhang
,
Pengyu Chen
Abstract
The aim of this paper is to discuss the existence of mild solutions for a class of semilinear stochastic partial differential equation with nonlocal initial conditions and noncompact semigroups in a real separable Hilbert space. Combined with the theory of stochastic analysis and operator semigroups, a generalized Darbo’s fixed point theorem and a new estimation technique of the measure of noncompactness, we obtained the existence of mild solutions under the situation that the nonlinear term and nonlocal function satisfy some appropriate local growth conditions and a noncompactness measure condition. In addition, the condition of uniformly continuity of the nonlinearity is not required and also the strong restriction on the constants in the condition of noncompactness measure is completely deleted in this paper. An example to illustrate the feasibility of the main results is also given.
This work was supported by NNSF of China (Grant No. 11501455), NNSF of China (Grant No. 11661071) and Key Project of Gansu Provincial National Science Foundation (Grant No. 1606RJZA015).
(Communicated by Michal Fečkan)
Acknowledgement
The authors would like to express sincere thanks to the anonymous referee for his/her carefully reading the manuscript and valuable comments and suggestions.
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© 2019 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Prof. RNDr. pavel brunovský, DrSc. passed away ∗dec. 5, 1934 – † dec. 14, 2018
- Ideals and congruences in pseudo-BCH algebras
- Regular double p-algebras
- Distributive nearlattices with a necessity modal operator
- States in generalized probabilistic models: An approach based in algebraic geometry
- Free power-associative n-ary groupoids
- On the 2-class field tower of subfields of some cyclotomic ℤ2-extensions
- On the space of generalized theta-series for certain quadratic forms in any number of variables
- Uniqueness and periodicity for meromorphic functions with partial sharing values
- Mild solution of stochastic partial differential equation with nonlocal conditions and noncompact semigroups
- An inverse boundary problem for fourth-order Schrödinger equations with partial data
- Entropy as an integral operator
- Global behavior of two third order rational difference equations with quadratic terms
- Measures on effect algebras
- Some topological and combinatorial properties preserved by inverse limits
- The convergence-theoretic approach to weakly first countable spaces and symmetrizable spaces
- Compositions of porouscontinuous functions
- A note on prime divisors of polynomials P(Tk); k ≥ 1
- On complete convergence for weighted sums of arrays of rowwise END random variables and its statistical applications
- Common fixed point theorems for a class of (s, q)-contractive mappings in b-metric-like spaces and applications to integral equations
Artikel in diesem Heft
- Prof. RNDr. pavel brunovský, DrSc. passed away ∗dec. 5, 1934 – † dec. 14, 2018
- Ideals and congruences in pseudo-BCH algebras
- Regular double p-algebras
- Distributive nearlattices with a necessity modal operator
- States in generalized probabilistic models: An approach based in algebraic geometry
- Free power-associative n-ary groupoids
- On the 2-class field tower of subfields of some cyclotomic ℤ2-extensions
- On the space of generalized theta-series for certain quadratic forms in any number of variables
- Uniqueness and periodicity for meromorphic functions with partial sharing values
- Mild solution of stochastic partial differential equation with nonlocal conditions and noncompact semigroups
- An inverse boundary problem for fourth-order Schrödinger equations with partial data
- Entropy as an integral operator
- Global behavior of two third order rational difference equations with quadratic terms
- Measures on effect algebras
- Some topological and combinatorial properties preserved by inverse limits
- The convergence-theoretic approach to weakly first countable spaces and symmetrizable spaces
- Compositions of porouscontinuous functions
- A note on prime divisors of polynomials P(Tk); k ≥ 1
- On complete convergence for weighted sums of arrays of rowwise END random variables and its statistical applications
- Common fixed point theorems for a class of (s, q)-contractive mappings in b-metric-like spaces and applications to integral equations
