Nonlocal Problem for a Third-Order Equation with Multiple Characteristics with General Boundary 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 problem with nonlocal conditions

Boundary Value Problem with Integral Conditions for a Linear Third-order Equation

On a Darboux Problem for a Third Order Hyperbolic Equation with Multiple Characteristics

A Darboux type problem for a model hyperbolic equation of the third order with multiple characteristics is considered in the case of two independent variables. The Banach space ◦ C 2,1 α , α ≥ 0, is introduced where the problem under consideration is investigated. The real number α0 is found such that for α > α0 the problem is solved uniquely and for α < α0 it is normally solvable in Hausdorff’...

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...