On the global existence and boundedness of solutions to a nonlinear integro-differential equations of second order

Abstract

The purpose of this paper is to study the global existence and boundedness of solutions to a kind of nonlinear integro-differential equations of second order by integral inequalities. Some illustrative examples are also provided. Our results complement and improve some ones in the literature.

Continuability and boundedness of solutions to a differential equation of third order with multiple deviating arguments

“…[9], Ademola vd. [10], Ademola [11], Ayhan [12], Ayhan ve Sofuoglu [13], Remili ve Oudjedi [14][15], Remili ve Beldjerd [16], Tunç ve Ayhan [17][18][19][20], Tunç [21] ve bu çalışmada atıfta bulunulan diğer çalışmalar incelenebilir. Bu çerçevede son zamanlarda Remili ve Beldjerd [16] tarafından ( ) > 0 olmak üzere ( ( ) ′ ) ′′ + ( ) ( ′ ) ′′ + ( ) ( ′ ) + ( )ℎ( ( − ( )) = ( , ( ), ( − ( ), ′ ( − ( ), ′′ ( ))…”

New results on exponential stability of nonlinear Volterra integro-differential equations with constant time-lag

“…That is, the trivial solution of (VIDE) (1.9) is (UEAS [3], [4]), Burton ([5], [6], [7]), Burton et al [8], Burton and Mahfoud ([9], [10]), Eloe et al [13], Furumochi and Matsuoka [14], Graef and Tunç [15], Graef et al [16], Grimmer and Seifert [17], Gripenberg et al [18], Hara et al [19], Islam and Raffoul [20], Jordan [21], Levin [22], Mahfoud [23], Miller [24], Raffoul ([25], [26], [27], [28]), Raffoul and Ren [29], Raffoul and Unal [29], Rama Mohana Rao and Raghavendra [30], Rama Mohana Rao and Srinivas [31], Staffans [32], Tunç ([33], [34], [35]) Tunç and Ayhan [38], Vanualailai and Nakagiri [39], Wang [40], Wazwaz [41], Zhang [42], Da Zhang [43].…”