Displaying similar documents to “Two approximation results for the parabolic singular perturbation problem”

Existence of nonzero nonnegative solutions of semilinear equations at resonance

Michal Fečkan (1998)

Commentationes Mathematicae Universitatis Carolinae

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The existence of nonzero nonnegative solutions are established for semilinear equations at resonance with the zero solution and possessing at most linear growth. Applications are given to nonlinear boundary value problems of ordinary differential equations.

Boundedness properties of resolvents and semigroups of operators

J. van Casteren (1997)

Banach Center Publications

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Let T: H → H be an operator in the complex Hilbert space H. Suppose that T is square bounded in average in the sense that there exists a constant M(T) with the property that, for all natural numbers n and for all x ∈ H, the inequality 1 / ( n + 1 ) ∑ j = 0 n ∥ T j x ∥ 2 ≤ M ( T ) 2 ∥ x ∥ 2 is satisfied. Also suppose that the adjoint T* of the operator T is square bounded in average with constant M(T*). Then the operator T is power bounded in the sense that s u p ∥ T i n ∥ : n ∈ ℕ is finite. In fact the following inequality is valid for all n ∈ ℕ: ∥Tn∥ ≤ e M(T)M(T*)....