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Iterative solution of nonlinear equations of the pseudo-monotone type in Banach spaces

A. M. Saddeek, Sayed A. Ahmed (2008)

Archivum Mathematicum

The weak convergence of the iterative generated by J ( u n + 1 - u n ) = τ ( F u n - J u n ) , n 0 , ( 0 < τ = min { 1 , 1 λ } ) to a coincidence point of the mappings F , J : V V is investigated, where V is a real reflexive Banach space and V its dual (assuming that V is strictly convex). The basic assumptions are that J is the duality mapping, J - F is demiclosed at 0 , coercive, potential and bounded and that there exists a non-negative real valued function r ( u , η ) such that sup u , η V { r ( u , η ) } = λ < ...

IVPs for singular multi-term fractional differential equations with multiple base points and applications

Yuji Liu, Pinghua Yang (2014)

Applicationes Mathematicae

The purpose of this paper is to study global existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. By constructing a special Banach space and employing fixed-point theorems, some sufficient conditions are obtained for the global existence and uniqueness of solutions of this kind of equations involving Caputo fractional derivatives and multiple base points. We apply the results to solve the forced logistic model with multi-term fractional...

Jacobi matrices on trees

Agnieszka M. Kazun, Ryszard Szwarc (2010)

Colloquium Mathematicae

Symmetric Jacobi matrices on one sided homogeneous trees are studied. Essential selfadjointness of these matrices turns out to depend on the structure of the tree. If a tree has one end and infinitely many origin points the matrix is always essentially selfadjoint independently of the growth of its coefficients. In case a tree has one origin and infinitely many ends, the essential selfadjointness is equivalent to that of an ordinary Jacobi matrix obtained by restriction to the so called radial functions....

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