In this section, we present the condition for non existence of non-trivial solution of (1).
Δ ℓ 2 u ( k ) + f ( k, u ( k ) ) = 0, k ∈ [ a, ∞ ), a > 0. and we prove the condition for non existence of non-trivial solution where Δ ℓ u ( k ) = u ( k + ℓ ) − u ( k ) for ℓ > 0. Further we present some formulae and examples to find the values of finite and infinite series in number theory as application of Δ ℓ. MSC 39A12, 39A70, 47B39, 39B60.
The philosopher Immanuel Kant touched on a similar point in his critique of the ontological argument for God (which states, broadly, that God is the greatest thing that could possibly be conceived of, and that since existence is greater than non-existence, for the concept to cohere God must necessarily exist).
For example, it does not give non-existence for 2-periodic solutions of (1), when f is 2-periodic.
Let us remark this parametric evolution comparison method to prove global non-existence for arbitrary data first introduced in [20], for scalar quasilinear heat equation.
Tartar and Murat [5 7] showed examples of the non-existence for such problems (see e.g. [8] also for the historical development).
For global existence and non-existence of solutions for the Cauchy problem of equation (1) with (rho(x)=1), (4) and a (possibly nonlinear) damping term, we here refer to [7 9].
This yields non-existence of optimizers for the problem over absolutely continuous measures.
The paper concludes by identifying some of the major barriers in more widespread use of RA in recycled aggregate concrete (RAC), including lack of awareness, lack of government support, non-existence of specifications/codes for reusing these aggregates in new concrete.
Moreover, the non-existence of solutions for a specified range of Reynolds numbers with a particular positive expanding ratio is discovered.
What geometric/topological, local/global conditions on the domain (Omega ) guarantee the existence (or non-existence) of extremals for (mu _{gamma, s}(Omega )), that is a function (u_Omega ) in (H^1_0(Omega )) such that (J^Omega _{gamma, s} u_{Omega })=mu _{gamma, s}(Omega ))?
