Positive solutions of nonlinear singular boundary value problem in abstract space

Multiple Solutions of Boundary Value Problems fornth-Order Singular Nonlinear Integrodifferential Equations in Abstract Spaces

“…But such equations do not have singular nonlinear terms. As much as we know, there are a few papers ( [10][11][12][13][14][15][16][17][18]) to consider the singular problems in abstract Banach spaces. In Liu [10], the following singular problems in Banach spaces − ( ) = ( , ( ) , ( )) , ∀0 < ≤ ; (0) = (0) = , (1) were investigated by constructing a special convex closed set and using Mönch fixed point theorem, where denotes the zero element of .…”

The Solutions of Mixed Monotone Fredholm-Type Integral Equations in Banach Spaces

“…Guo and Lakshmikantham [1] introduced the definition of mixed monotone operator and coupled fixed point; there are many good results (see [1][2][3][4][5][6][7][8][9][10][11][12][13]). In the special case where ( , , ) is nondecreasing in for fixed , ∈ , Guo [2] established an existence theorem of the maximal and minimal solutions for (1) in the ordered Banach spaces by means of monotone iterative techniques.…”

“…But these all required the compactness conditions and the monotone conditions in the above papers, and furthermore they did not obtain the unique solutions. In addition, extensive studies have also been carried out to study the global or iterative solutions of initial value problems [8][9][10][11][12][13].…”

Existence of positive solutions for singular four-point boundary value problem with a p-Laplacian

“…They also appear in the study of positive radial solutions of nonlinear elliptic equations. Therefore, they have been extensively studied in recent years, see, for instance, [1]- [5], [8], [13] and references therein. After studying singular two-point BVPs in detail, some authors began to pay attention to singular multi-point BVPs [9]- [12], [14]- [17].…”