Sentence examples for deduce existence from inspiring English sources

As applications we prove the strong Hodge de Rahm Kodaira decomposition for forms in Lp and deduce existence and regularity results for the solutions of the Hodge and de Rham equations in Lp.

In 1967, Kiguradze [18] proved that it is enough to consider a one-sided Nagumo condition (by eliminating the absolute value in (1.11)) to deduce existence results for Dirichlet problems.

So, to deduce existence results for this new situation, it is necessary to make use of the qualitative properties of continuity and monotonicity of the functions that define the nonlinear boundary value conditions.

To deduce existence results for (2.8) they consider a variant of the truncated problem (1.14) (by adding the term tanh ) coupled with the following nonconstant Dirichlet boundary conditions: (2.11).

This extension is carried out in the next section and will then be applied to deduce existence of solutions for greater classes of problems among which we find the following one, which we shall study in detail as an example: x ″ = ϕ 1 / 3 ( 1 t 2 + | x | ) a.e.

Ibn Daud deviates significantly from his predecessors since he does not deduce the existence of God from creation.

1981), the eminent philosopher and commentator, argues that Mulla Sadra does not provide a demonstration but rather an assertoric argument because in effect all proofs for the existence of God begin with his effects and deduce his existence as the cause of those effects.

From the fixed alternative, we deduce the existence of a fixed point of, that is, the existence of a mapping such that for each.

From the fixed point alternative, we deduce the existence of a fixed point of, that is, the existence of a mapping such that for each.

Using the fixed point alternative we deduce the existence of a fixed point of J, that is, the existence of a mapping C : X → Y such that C(2x) = 8C x), for all x ∈ X.

It follows that d s ( f, J f ) ≤ α 2. Using the fixed-point alternative we deduce the existence of a fixed point of J, that is, the existence of a mapping T : X → Y such that T ( x 2 ) = T ( x ) 2. for all x ∈ X.