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Existence of solutions of impulsive boundary value problems for singular fractional differential systems

Yuji Liu (2017)

Mathematica Bohemica

A class of impulsive boundary value problems of fractional differential systems is studied. Banach spaces are constructed and nonlinear operators defined on these Banach spaces. Sufficient conditions are given for the existence of solutions of this class of impulsive boundary value problems for singular fractional differential systems in which odd homeomorphism operators (Definition 2.6) are involved. Main results are Theorem 4.1 and Corollary 4.2. The analysis relies on a well known fixed point...

Existence results for q-difference inclusions with three-point boundary conditions involving different numbers of q

Sotiris K. Ntouyas, Thanin Sitthiwirattham, Jessada Tariboon (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we study a new class of three-point boundary value problems of nonlinear second-order q-difference inclusions. Our problems contain different numbers of q in derivatives and integrals. By using fixed point theorems, some new existence results are obtained in the cases when the right-hand side has convex as well as noncovex values.

Existence theory for single and multiple solutions to singular positone discrete Dirichlet boundary value problems to the one-dimension p -Laplacian

Daqing Jiang, Li Li Zhang, Donal O'Regan, Ravi P. Agarwal (2004)

Archivum Mathematicum

In this paper we establish the existence of single and multiple solutions to the positone discrete Dirichlet boundary value problem Δ [ φ ( Δ u ( t - 1 ) ) ] + q ( t ) f ( t , u ( t ) ) = 0 , t { 1 , 2 , , T } u ( 0 ) = u ( T + 1 ) = 0 , where φ ( s ) = | s | p - 2 s , p > 1 and our nonlinear term f ( t , u ) may be singular at u = 0 .

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