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Some generic properties of nonlinear second order diffusional type problem

Vladimír Ďurikovič, Mária Ďurikovičová (1999)

Archivum Mathematicum

We are interested of the Newton type mixed problem for the general second order semilinear evolution equation. Applying Nikolskij’s decomposition theorem and general Fredholm operator theory results, the present paper yields sufficient conditions for generic properties, surjectivity and bifurcation sets of the given problem.

Some surjectivity theorems with applications

H. K. Pathak, S. N. Mishra (2013)

Archivum Mathematicum

In this paper a new class of mappings, known as locally λ -strongly φ -accretive mappings, where λ and φ have special meanings, is introduced. This class of mappings constitutes a generalization of the well-known monotone mappings, accretive mappings and strongly φ -accretive mappings. Subsequently, the above notion is used to extend the results of Park and Park, Browder and Ray to locally λ -strongly φ -accretive mappings by using Caristi-Kirk fixed point theorem. In the sequel, we introduce the notion...

Stability of solutions for an abstract Dirichlet problem

Marek Galewski (2004)

Annales Polonici Mathematici

We consider continuous dependence of solutions on the right hand side for a semilinear operator equation Lx = ∇G(x), where L: D(L) ⊂ Y → Y (Y a Hilbert space) is self-adjoint and positive definite and G:Y → Y is a convex functional with superquadratic growth. As applications we derive some stability results and dependence on a functional parameter for a fourth order Dirichlet problem. Applications to P.D.E. are also given.

Stabilization of solutions to a differential-delay equation in a Banach space

J. J. Koliha, Ivan Straškraba (1997)

Annales Polonici Mathematici

A parameter dependent nonlinear differential-delay equation in a Banach space is investigated. It is shown that if at the critical value of the parameter the problem satisfies a condition of linearized stability then the problem exhibits a stability which is uniform with respect to the whole range of the parameter values. The general theorem is applied to a diffusion system with applications in biology.

Superposition operator on the space of sequences almost converging to zero

Egor Alekhno (2012)

Open Mathematics

We study the superposition operator f on on the space ac 0 of sequences almost converging to zero. Conditions are derived for which f has a representation of the form f x = a+bx +g x, for all x ∈ ac 0 with a = f 0, b ∈ D(ac 0), g a superposition operator from ℓ∞ into I(ac 0), D(ac 0) = {z: zx ∈ ac 0 for all x ∈ ac 0}, and I(ac 0) the maximal ideal in ac 0. If f is generated by a function f of a real variable, then f is linear. We consider the conditions for which a bounded function f generates f...

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