Abstract In this paper, governed by the fundamental solutions we introduce the Green’s function of the second-order differential equations in general form with respect to boundary conditions and deal with… Click to show full abstract
Abstract In this paper, governed by the fundamental solutions we introduce the Green’s function of the second-order differential equations in general form with respect to boundary conditions and deal with the solvability of the infinite system of second-order differential equations with p, q ∈ C([0, T ], ℝ) and the boundary conditions u i (0) = u i (T ) = 0. We remark that the subjected system has not been previously considered and this investigation complements several results in the literature. Using the ideas of Hausdorff measure of noncompactness and Meir-Keleer condensing operator we seek the sufficient conditions to justify the existence of solutions for the aforementioned system in Banach sequence space ℓ p (1 ≤ p < ∞). Finally, an example is given to ascertain the efficiency of the results.
               
Click one of the above tabs to view related content.