Displaying similar documents to “Factorization of matrix-functions and regularization of singular integral operators on manifolds with boundary.”

Positive solutions to nonlinear singular second order boundary value problems

Gabriele Bonanno (1996)

Annales Polonici Mathematici

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Existence theorems of positive solutions to a class of singular second order boundary value problems of the form y'' + f(x,y,y') = 0, 0 < x < 1, are established. It is not required that the function (x,y,z) → f(x,y,z) be nonincreasing in y and/or z, as is generally assumed. However, when (x,y,z) → f(x,y,z) is nonincreasing in y and z, some of O'Regan's results [J. Differential Equations 84 (1990), 228-251] are improved. The proofs of the main theorems are based on a fixed point...

On complete solutions and complete singular solutions of second order ordinary differential equations

Masatomo Takahashi (2007)

Colloquium Mathematicae

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A complete solution of an implicit second order ordinary differential equation is defined by an immersive two-parameter family of geometric solutions on the equation hypersurface. We show that a completely integrable equation is either of Clairaut type or of first order type. Moreover, we define a complete singular solution, an immersive one-parameter family of singular solutions on the contact singular set. We give conditions for existence of a complete solution and a complete singular...

On a Question of Pełczyński about Strictly Singular Operators

Jesús M. F. Castillo, Marilda Simoes, Jesús Suárez de la Fuente (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

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We exhibit new examples of weakly compact strictly singular operators with dual not strictly cosingular and characterize the weakly compact strictly singular surjections with strictly cosingular adjoint as those having strictly singular bitranspose. We then obtain new examples of super-strictly singular quotient maps and show that the strictly singular quotient maps in Kalton-Peck sequences are not super-strictly singular.

Boundary value problems and singular integral equations on Banach function spaces

E. M. Rojas

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We study the solvability and Fredholmness of binomial boundary value problems for analytic functions represented by integrals of Cauchy type with density on abstract nonstandard Banach function spaces, assuming continuous, piecewise continuous and essentially bounded factorizable functions as coefficients. The representation of the solutions of those problems allows us to describe the explicit form of the solutions of the associated singular integral equations in each case. The solvability...