Sentence examples for problems for the following from inspiring English sources

In this section, we consider exponentially practical stability problems for the following four cases: a discrete time system with disturbance, a discrete time singular system with disturbance, a discrete time system with delay and disturbance, and a discrete time singular system with delay and disturbance.

In this paper, we consider singular boundary value problems for the following nonlinear fractional differential equations with delay: left { textstylebegin{array}{l@{quad}l} D^{alpha}x t)+lambda f (t,x t-tau) )=0,x t-tau,1)backslash {tau}, x(t)=0ta(t), &tin 0,1 backslash)=x'(0)=0, end{tau}y}displaystyle right.

We restrict ourselves to the Dirichlet and Neumann problems for the following Laplace equation: Δ u : = ( ∂ / ∂x ) 2 u + ( ∂ / ∂y ) 2 u = 0, Open image in new window (1). in a simply connected domain D Open image in new window with boundary C Open image in new window in the plane of variables ( x, y ) ∈ R 2 Open image in new window.

In 2011, Rehman [12] studied the existence and uniqueness of solutions to nonlinear three-point boundary value problems for the following fractional differential equation: where 1 < δ < 2, 0 < σ < 1, α, β ∈ R, α η ( 1 − β ) + ( 1 − α ) ( t − β η ) ≠ 0 and D 0 + δ C, D 0 + σ C denote Caputo fractional derivatives.

Claiming that belief attributions are not metaphysically de re is problem, for the following reasons.

In this paper, we investigate the stability problem for the following functional inequality: (12).

with the norm Consider the following nonlocal Cauchy problem for the following fractional differential equation in : (42).

We investigate the stability problem for the following functional inequality on restricted domains of Banach modules over a -algebra.

In this paper, we consider the initial boundary value problem for the following degenerate Kirchhoff equations with strong damping and source terms: (1.1).

In this paper, we discuss the existence of solutions to the nonlocal Cauchy problem for the following fractional differential equations in a Banach space : (11).

By using fixed point theorems in cones, the existence of multiple positive solutions is considered for nonlinear -point boundary value problem for the following second-order boundary value problem on time scales,,,, where is an increasing homeomorphism and homomorphism and.