Sentence examples for boundary value problem were from inspiring English sources

The existence results for the above boundary value problem were obtained by using the upper and lower solutions method associated with the Schauder fixed point theorem.

In [3, 4], through the use of Guo-Krasnosel'skii's fixed point theorem, the existence and multiplicity of positive solutions for the following periodic boundary value problem were established.

Recently, the existence of solutions for impulsive fractional q-difference equations with antiperiodic boundary conditions was discussed in [15], whereas the existence results for a nonlinear impulsive (q_{k} -integral boundary value problem were obtained in [16].

The sufficient conditions to guarantee the existence of at least three positive solutions of the above multi-point boundary value problem were established by using a new fixed point theorem obtained in [19].

For the one-dimensional case, when the liquid is incompressible and the gas is polytropic, the global existence and uniqueness of a weak solution to the free boundary value problem were studied in [6 9].

A nonlinear boundary value problem is studied as an example.

The dimensionless emerging linearized electro-magnetic boundary value problem is solved using integral methods.

Closed-form solutions for the linearized dimensionless boundary value problem are derived.

The resulting boundary value problem was solved analytically via the generalized integral transform technique (GITT).

In this paper, a boundary value problem is studied as an example.

The non-self-adjoint boundary value problem is formulated with the Euler-Bernoulli theory and an associated adjoint boundary value problem is introduced.