Sentence examples for boundary value problem exists from inspiring English sources

They established the following result: if a nontrivial continuous solution to the above fractional boundary value problem exists, then int_{a}^{b} (b-s)^{alpha-beta-1} biglvert q(s bigrvert,dsgeq frac{ b-a)^{-beta}}{max {frac{ b-aamma(alpha)}-frac {Gamma(2-beta)}{Gamma(alpha-beta)},frac{Gamma(2-beta )}{Gamma(alpha-beta)}, (frac{2-alpha}{alpha-1} )frac{Gamma(2-beta)}{Gamma(alpha-beta)} }}.

However, a finite solution to the boundary value problem exists only if the traction forces perfectly cancel one another over the cluster area.

Several generalizations and extensions of inequality (1.2) to different boundary value problems exist in the literature.

Applications of mixed boundary value problems exist in large numbers in classical mathematical physics, physical geodesy, electro-magnetics, analysis of measurement [1, 2], and specific boundary problems such as the Dirichlet problem and the Neumann problem [3].

If a nontrivial continuous solution of the fractional boundary value problem (1.9) exists, then int_{a}^{b} (b-s)^{alpha-beta-1} biglvert q(s bigrvert, ds geq frac{ b-a)^{-beta}}{max {frac{ b-aamma(alpha)} - frac{Gamma(2-beta)}{Gamma(alpha-beta)}, frac{Gamma(2-beta )}{Gamma(alpha-beta)}, frac{2-alpha}{alpha-1} cdot frac{Gamma(2-beta)}{Gamma(alpha-beta)} }}.

Different from [7], [9] is not based on the assumption that the upper and lower solutions to the boundary value problem should exist, but constructs the specific form of the symmetric upper and lower solutions.

Returning to overdetermined boundary value problems, there exists a large amount of literature dealing with the subject; in general, these problems are prescribed by a classical partial differential equation where both Dirichlet and Neumann boundary conditions are imposed on the boundary of the domain.

Particularly, when (f(mathbf{x})) is just an invertible Clifford constant, for the boundary value problem (4.1) there exists a unique solution.

Condition by virtue of Theorem of the paper [14] implies that Green's function G of the boundary value problem (3.2). exists and satisfies the inequalities for while for.

The aim is to find those parameters ( Re, We, Fr ) for which a solution of the boundary value problem of Category (A) exists with a ( 1 ) = 0.

Definition 2.2 If for the system (1) with boundary conditions (2) there exists at least one solution, the boundary value problem (1 - 2) is said to be consistent.