Sentence examples for boundary value problems exist from inspiring English sources

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].

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.

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.

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.

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)} }}.

However, there exist some papers considered the boundary value problems of fractional differential equations; see [10 22].

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.

In [14], Kaufmann and Kosmatov showed that there exist countably many positive solutions for the two-point boundary value problems with infinitely many singularities of following form: (1.2).