Existence results of solutions for a neutral evolution equation with nonlocal conditions on infinite interval

Authors：Cao, Nan; Fu, Xianlong^*

Source：Journal of Mathematical Analysis and Applications, 2022, 510(1): 126008.

DOI：10.1016/j.jmaa.2022.126008

• Evolution equation
• Nonlocal condition
• Analytic semigroup
• Fractional power
• Regularity
• 18dz2271000)

This paper focuses on the study of existence and regularity of solutions for a semi-linear neutral differential equation defined on [0, +infinity) with state dependent nonlocal condition. The existence and regularity of solutions on infinite interval of the considered equation, including the existence of Holder continuous solutions, are respectively investigated by the theory of fractional power operators and fixed point theorems under some conditions for the nonlinear functions. An example is also provided to illustrate the applications of the obtained results.