An abstract monotone iterative technique

The Monotone Iterative Technique for Three-Point Second-Order Integrodifferential Boundary Value Problems with p-Laplacian

“…The details of the monotone iterative method can be found in [20][21][22][23][24][25][26][27] and for the abstract monotone iterative method, see [28,29]. To the best of the authors' knowledge, this is the first paper dealing with the integrodifferential equations in the present configuration.…”

On Discontinuous First Order Implicit Boundary Value Problems

“…Classical comparison theorems and maximum principles (cf., e.g., [22]) do not apply since g is allowed to be discontinuous with respect to both of its variables. In Section 4 the BVP (1.1) is transformed into the general framework (1.4), and the existence of extremal solutions of this transformed equation within an order interval of W is proved.…”

“…In the study of the operator equation of the form Lu=Nu it is usually assumed that L is a linear operator, and that N is continuous (cf. [22]). These assumptions would yield essentially more restrictive hypotheses in the next applications.…”

Fixed point theorems for monotone operators in ordered Banach spaces with h-ordering differences

“…In the past several decades, monotone operators in ordered Banach spaces have been studied extensively, and many new fixed point theorems have been established; see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references therein. Most of these new results have been proved based on the cone theory and monotone iterative technique.…”