Positive Solutions for Nonlinear Differential Equations with Periodic Boundary Condition

Positive Solutions for Nonlinear Differential Equations with Periodic Boundary Condition

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, ...

Positive Solutions of Second Order Nonlinear Differential Equations with Periodic Boundary Value Conditions

Criteria are established for existence of positive solutions to the second order periodic boundary value problem −u(t) + pu(t) + p1u(t) = f(t, u), t ∈ I = [0, T ], u(0) = u(T ), u(0) = u(T ), where p ∈ R and p1 ≥ 0. The discussion is based on the fixed point index theory in cones. AMS Subject Classification: 34B18

Positive Periodic Solutions In Neutral Nonlinear Differential Equations

We use Krasnoselskii’s fixed point theorem to show that the nonlinear neutral differential equation with delay d dt [x(t)− ax(t− τ)] = r(t)x(t)− f(t, x(t− τ)) has a positive periodic solution. An example will be provided as an application to our theorems. AMS Subject Classifications: 34K20, 45J05, 45D05

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 aclass 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, ∞...