The aftermath of the intermediate value theorem.
The Approximation of Generalized Turning Points by Projection Methods with Superconvergence to the Critical Parameter.
The Cauchy problem for the nonlinear Schrödinger Equation in H1.
The coincidence index for fundamentally contractible multivalued maps with nonconvex values
We study a coincidence problem of the form A(x) ∈ ϕ (x), where A is a linear Fredholm operator with nonnegative index between Banach spaces and ϕ is a multivalued A-fundamentally contractible map (in particular, it is not necessarily compact). The main tool is a coincidence index, which becomes the well known Leray-Schauder fixed point index when A=id and ϕ is a compact singlevalued map. An application to boundary value problems for differential equations in Banach spaces is given.
The comparison of the convergence speed between Picard, Mann, Krasnoselskij and Ishikawa iterations in Banach spaces.
The concentration-compactness principle in the calculus of variations. The locally compact case, part 1
The convergence of an implicit mean value iteration.
The convergence of mean value iteration for a family of maps.
The Dependence of Critical Parameter Bounds on the Monotonicity of a Newton Sequence.
The effect of rounding errors on a certain class of iterative methods
In this study we are concerned with the problem of approximating a solution of a nonlinear equation in Banach space using Newton-like methods. Due to rounding errors the sequence of iterates generated on a computer differs from the sequence produced in theory. Using Lipschitz-type hypotheses on the mth Fréchet derivative (m ≥ 2 an integer) instead of the first one, we provide sufficient convergence conditions for the inexact Newton-like method that is actually generated on the computer. Moreover,...
The eigenvalue problem for a singular quasilinear elliptic equation.
The equivalence between -stabilities of the Krasnoselskij and the Mann iterations.
The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous -strongly accretive operators in uniformly smooth Banach spaces.
The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions.
The equivalence between the -stabilities of Picard–Banach and Mann–Ishikawa iterations.
The equivalence of Mann iteration and Ishikawa iteration for -uniformly pseudocontractive or -uniformly accretive maps.
The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators.
The Euler-Lagrange inclusion in Orlicz-Sobolev spaces
We establish the Euler-Lagrange inclusion of a nonsmooth integral functional defined on Orlicz-Sobolev spaces. This result is achieved through variational techniques in nonsmooth analysis and an integral representation formula for the Clarke generalized gradient of locally Lipschitz integral functionals defined on Orlicz spaces.
The existence and uniqueness of solution of Duffing equations with non- perturbation functional at nonresonance.
The existence of bounded solutions for differential equations in Hilbert spaces
The existence of bounded solutions for equations x' = A(t)x + r(x,t) is proved, where the linear part is exponentially dichotomic and the nonlinear term r satisfies some weak conditions.