Quadratic approximation of solutions for differential equations with nonlinear boundary conditions

Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations

This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ...

Ordinary Differential Equations with Nonlinear Boundary Conditions

The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems. 2000 Mathematics Subject Classification: 34A45, 34B15, 34A40.

Positive Solutions for Nonlinear Differential Equations with Periodic Boundary Condition

Existence of Solutions of Multi-Point BVPs for Impulsive Functional Differential Equations with Nonlinear Boundary Conditions

Two classes of multi-point BVPs for first order impulsive functional differential equations with nonlinear boundary conditions are studied. Sufficient conditions for the existence of at least one solution to these BVPs are established, respectively. Our results generalize and improve the known ones. Some examples are presented to illustrate the main results. c ©2012 NGA. All rights reserved.

Existence of Solutions for Nonlinear Fractional Integro-Differential Equations with Three-Point Nonlocal Fractional Boundary Conditions

Fractional calculus differentiation and integration of arbitrary order is proved to be an important tool in the modelling of dynamical systems associated with phenomena such as fractal and chaos. In fact, this branch of calculus has found its applications in various disciplines of science and engineering such as mechanics, electricity, chemistry, biology, economics, control theory, signal and i...