Abstract In the work (Bouaouid et al. in Adv. Differ. Equ. 2019:21, 2019), authors have used Krasnoselskii fixed point theorem for showing existence of mild solutions an abstract class conformable fractional differential equations form: $\frac{d^{\alpha }}{dt^{\alpha }}[\frac{d^{\alpha }x(t)}{dt^{\alpha }}]=Ax(t)+f(t,x(t))$ <...

and Applied Analysis 3 solutions for singular second-order m-point boundary value problem, in 11 Leggett and Williams discussed the nonlinear equation modelling certain infectious diseases. In 12 Zima discussed a three-point boundary value problem for second-order ordinary differential equations. In 13, 14 the authors proved multiplicity of positive radial solutions for an elliptic system on an...

This paper is concerned with a general existence and continuous dependence of mild solutions to semilinear functional differential equations with infinite delay in Banach spaces. In particular, our results are applicable to the equations whose Co-semigroups and nonlinear operators, defined on an open set, are noncompact. Introduction. Let £ be a Banach space over the real field R with norm | | ...

and Applied Analysis 3 where τ, p, g : R → R are continuous functions, B, δ, C are constants, τ and p are T -periodic, C/ 0, |B|/ 1, and T > 0. Zhou and Zhang 8 extended the results in 1 to the higher-order neutral functional differential equation with positive and negative coefficients: d dtn [ x t px t − τ ] −1 n 1 P t x t − σ −Q t x t − δ 0, t ≥ t0, 1.9 where p ∈ R \ {±1}, τ, σ, δ ∈ R and P,...

Let …A0;A1† and …B0;B1† be couples of quasi-Banach spaces and let T be a linear operator. We prove that if T : A0 ! B0 is compact and T : A1 ! B1 is bounded, then T : …A0;A1† ;q ! …B0;B1† ;q is also compact. Some results on the structure of minimal and maximal interpolation methods are also established. 0. Introduction. Assume that T is a linear operator such that T : Lp0 ! Lq0 compactly and T ...