In this article, we investigate sufficient conditions for existence of maximal and minimal solutions to a coupled system of highly nonlinear differential equations of fractional order with mixed type boundary conditions. To achieve this goal, we apply monotone iterative technique together with the method of upper and lower solutions. Also an error estimation is given to check the accuracy of th...

Weakly harmonic maps from a domain Ω⊂Rd, d≥2 (the upper half-space R+d or bounded C1,α domain, α∈(0,1]) into smooth closed manifold are studied. Prescribing small Dirichlet data in either of the classes L∞(∂Ω) BMO(∂Ω), we establish solvability resulting boundary value problems by means nonvariational method. As by-product, solutions shown to be locally smooth, Cloc∞. Moreover, show that can cho...

  Background: Although upper-extremity disability correlates with psychosocial aspects of illness the association with sleep disturbance in upper extremity disability is less certain. To evaluate whether sleep disturbance is associated with upper-extremity disability among patients with upper extremity illness, accounting for sociodemographic, condition-related, and psychosocial factors. Method...

r–division approach pieces of size O(r) with boundary O( √ r) per piece (total boundary O(n/ √ r)) precompute APSP for all nodes on the boundary, space O(n/r); at query time, explore piece of v (say Pv) and piece of w (Pw) and find best connection pair ∂Pv × ∂Pw, piece sizes O(r) and O( √ r) connection pairs, total query time O(r) smoothly interpolates between SSSP and APSP (only separators use...

In this paper, we consider the existence of extreme solutions of the boundary value problem for a fractional order differential equation Dδu = f(t, u), t ∈ [0, T ], 0 < δ < 1, 0 < T < ∞, with a nonlinear boundary conditions g(u(0)) = u(T ). Under a lower solution α and un upper solution β with β ≤ α, we establish existence results of extreme solutions by means of the method of upper and lower s...

This paper concerned with the existence of solutions of anti-periodic boundary value problems for impulsive differential equations with φ-Laplacian operator. Firstly, the definition a pair of coupled lower and upper solutions of the problem is introduced. Then, under the approach of coupled upper and lower solutions together with Nagumo condition, we prove that there exists at least one solutio...

In general, the value function associated with an exit time problem is a discontin-uous function. We prove that the lower (upper) semicontinuous envelope of the value function is a supersolution (subsolution) of the Hamilton-Jacobi equation involving the proximal subdiierentials (superdiierentials) with subdiierential type (superdiierential type) mixed boundary condition. We also show that if t...

In general, the value function associated with an exit time problem is a discontinuous function. We prove that the lower (upper) semicontinuous envelope of the value function is a supersolution (subsolution) of the Hamilton–Jacobi equation involving the proximal subdifferentials (superdifferentials) with subdifferential-type (superdifferential-type) mixed boundary condition. We also show that i...

In this paper, we study the concept of S-approximation spaces in fuzzy set theory and investigate its properties. Along introducing three pairs of lower and upper approximation operators for fuzzy S-approximation spaces, their properties under different assumptions, e.g. monotonicity and weak complement compatibility are studied. By employing two thresholds for minimum acceptance accuracy and m...