Uniqueness, existence, and optimality for fourth-order Lipschitz equations

On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order

“…Later, Henderson [42] studied this question for k-point right focal boundary value problems for nth-order ordinary differential equations. Other uniqueness implies uniqueness results are found in the papers by Clark and Henderson [43], Ehme and Hankerson [44], Henderson and McGwier [45],and Peterson [46]. For the fourth-order equation, Peterson [47] firstly showed that uniqueness of solutions of four-point ''conjugate" boundary value problems is equivalent to uniqueness of both two-point and three-point ''conjugate" boundary value problems.…”

Optimal interval lengths for nonlocal boundary value problems associated with third order Lipschitz equations

“…These works were later adapted to the context of several types of nonlinear boundary value problems by Jackson [24,25], Eloe and Henderson [13], Hankerson and Henderson [19], and Henderson et al [21][22][23].…”

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

“…These works were later adapted by Jackson to determine optimal intervals for uniqueness of solutions (when solutions exist) for, respectively, conjugate boundary-value problems [28] and right focal boundary-value problems [29]. Following that, other optimality results employing the adapted methods of Melentsova and Mil shtein have been obtained in the context of several types of nonlinear boundaryvalue problems (see [8,10,14,20,23]).…”