A third-order nonlocal problem with nonlocal conditions

A third-order nonlocal problem with nonlocal conditions

Mixed Problem with Nonlocal Boundary Conditions for a Third-order Partial Differential Equation of Mixed Type

We study a mixed problem with integral boundary conditions for a third-order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on two-sided a priori estimates and on the density of the range of the operator generated by the considered problem. 2000 Mathematics Subject Classification. 35B45, 35K20, 35M10.

A Third Order Nonlocal Boundary Value Problem at Resonance

We consider the third-order nonlocal boundary value problem u ′′′ (t) = f (t, u(t)), a.e. in (0, 1), u(0) = 0, u ′ (ρ) = 0, u ′′ (1) = λ[u ′′ ], where 0 < ρ < 1, the nonlinear term f satisfies Carathéodory conditions with respect to L 1 [0, T ], λ[v] = 1 0 v(t) dΛ(t), and the functional λ satisfies the resonance condition λ[1] = 1. The existence of a solution is established via Mawhin's coincid...

Second-order Sufficient Optimality Conditions for a Semilinear Optimal Control Problem with Nonlocal Radiation Interface Conditions

We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffusegray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local op...

Positive solutions for singular third-order nonhomogeneous boundary value problems with nonlocal boundary conditions

Under various weaker conditions, we establish various results on the existence and nonexistence of positive solutions for singular third-order nonhomogeneous boundary value problems with nonlocal boundary conditions. The arguments are based upon the fixed point theorem of cone expansion and compression. Finally, we give two examples to demonstrate our results. Key–Words: Positive solutions, Fix...