Third order problems with nonlocal conditions of integral type

A third-order nonlocal problem with nonlocal conditions

Nonlocal boundary value problems of fractional order at resonance with integral conditions

*Correspondence: [email protected] Department of Basic Teaching, Tangshan University, Tangshan, Hebei 063000, People’s Republic of China Abstract Based upon the well-known coincidence degree theory of Mawhin, we obtain some new existence results for a class of nonlocal fractional boundary value problems at resonance given by { D0+u(t) = f (t,u(t),D α–1 0+ u(t),D α–2 0+ u(t)), t ∈ (0, 1), I3–α 0...

Existence and iteration of monotone positive solutions for third-order nonlocal BVPs involving integral conditions

This paper is concerned with the existence of monotone positive solution for the following third-order nonlocal boundary value problem u′′′ (t)+f (t, u (t) , u′ (t)) = 0, 0 < t < 1; u (0) = 0, au′ (0) − bu′′ (0) = α[u], cu′ (1) + du′′ (1) = β[u], where f ∈ C([0, 1] × R+ × R+, R+), α[u] = ∫ 1 0 u(t)dA(t) and β[u] = ∫ 1 0 u(t)dB(t) are linear functionals on C[0, 1] given by Riemann-Stieltjes inte...

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...

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.