New Existence Results and Comparison Principles for Impulsive Integral Boundary Value Problem with Lower and Upper Solutions in Reversed Order

Abstract

This paper investigates the existence of the extremal solutions to the integral boundary value problem for first-order impulsive functional integrodifferential equations with deviating arguments under the assumption of existing upper and lower solutions in the reversed order. The sufficient conditions for the existence of solutions were obtained by establishing several new comparison principles and using the monotone iterative technique. At last, a concrete example is presented and solved to illustrate the obtained results.

The Cădariu-Radu Method for Existence, Uniqueness and Gauss Hypergeometric Stability of Ω-Hilfer Fractional Differential Equations

“…Using the Diaz-Margolis theorem (i.e., Theorem 3), we obtain a new stability approximation result for (2), for more details, we refer to [13][14][15][16][17][18][19][20][21][22][23][24]. In these sources, one can find new problems.…”

Periodic Boundary Value Problems for First-Order Impulsive Functional Integrodifferential Equations with Integral-Jump Conditions

“…Monotone iterative technique coupled with the method of upper and lower solutions has provided an effective mechanism to prove constructive existence results for initial and boundary value problems for nonlinear differential equations; see [6]. However, many papers have studied applications of the monotone iterative technique to impulsive problems; see, for example, [7][8][9][10][11][12][13][14][15]. In those articles, the authors assumed that Δ ( ) = ( ( − )), that is, a short-term rapid change of the state (jump condition) at impulse point , depends on the left side of the limit of ( ).…”