Sturm-Liouville eigenvalue problems on time scales

Existence of Weak Solutions for Second-Order Boundary Value Problem of Impulsive Dynamic Equations on Time Scales

“…The study of boundary value problems for dynamic equations on time scales has recently received a lot of attention, see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] . At the same time, there have been significant developments in impulsive differential equations, see the monographs of Lakshmikantham et al 17 and Samoȋlenko and Perestyuk 18 .…”

Principal Eigenvalues of a Second-Order Difference Operator with Sign-Changing Weight and Its Applications

“…For the other recent results on the spectrum structure of discrete linear eigenvalue problems with one-sign weight, see Sun and Shi [11], Shi and Chen [12], Jirari [13], Bohner [14], and Agarwal et al [15] and the references therein.…”

Impulsive Diffusion Equation on Time Scales

“…The first studies on these type problems for linear ∆− differential equations on T were fulfilled by Chyan, Davis, Henderson and Yin [8] in 1998 and Agarwal, Bohner and Wong [9] in 1999. In [8], the theory of positive operators according to a cone in a Banach space is applied to eigenvalue problems related to the second order linear ∆−differential equations on T to prove existence of a smallest positive eigenvalue and then a theorem proved to compare the smallest positive eigenvalue for two problems of that type.…”

“…In [8], the theory of positive operators according to a cone in a Banach space is applied to eigenvalue problems related to the second order linear ∆−differential equations on T to prove existence of a smallest positive eigenvalue and then a theorem proved to compare the smallest positive eigenvalue for two problems of that type. In [9], an oscillation theorem is given for Sturm-Liouville (SL) eigenvalue problem on T with separated boundary conditions and Rayleigh's principle is studied. In 2002, Agarwal, Bohner and O'Regan [10] presented some new existence results for time scale BVP's on infinite intervals.…”