Multiple positive solutions of quasi-linear boundary value problems for finite difference equations

Three positive solutions of nonhomogeneous multi-point BVPs for second order p-Laplacian functional difference equations

“…(ii) T x ∈ P for each x ∈ P ; (iii) x is a solution of BVP (1) if and only if x is a solution of the operator equation x = T x; (iv) T : P → P is completely continuous.…”

“…In the known papers, the explicit expressions of the associated Green's functions are used to get multiple positive solutions of the two point or three point BVPs of difference equations by using Krasnosel'skii fixed point theorem [5][6][7][8], two-fixedpoint theorems in cones in Banach spaces [3,[9][10][11][12]19], three-fixed-point theorems [1,2,[13][14][15][16][17][18], the Linking Theorem and the Mountain Pass Lemma in the critical point theory [4,[23][24][25][26][27], the Five Functionals Fixed Point Theorem [28][29][30][31][32][33] and so on.…”

Studies on Nonhomogeneous Multi-point BVPs of Difference Equations with One-Dimensional p-Laplacian

“…In recent years, there has been a large number of papers interested in proving the existence of multiple positive solutions of the boundary value problems (BVPs for short) of the difference equations by using the associated Green s functions and the different fixed point theorems in cones in Banach spaces, see the papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and the references therein. However, one finds that all boundary conditions of BVPs involved are homogeneous.…”

Right focal boundary value problems for difference equations

“…For well over a decade, substantial results have been obtained for positive solutions and multiple positive solutions for boundary value problems for finite difference equations; see, for example [2,5,10,11,13,15,16,[20][21][22][23][25][26][27][28].…”