Sentence examples for under appropriate hypotheses from inspiring English sources

There is again an important class of theorems that guarantee the existence of certain choices under appropriate hypotheses.

Under appropriate hypotheses, they established the local existence and uniqueness of its solution.

Under appropriate hypotheses, we are able to build interval observers giving dynamic bounds containing the variables to estimate.

Moreover, as p is close to 2, we get the fourth nontrivial solution under appropriate hypotheses, where f x,u) satisfies Ambrosetti Rabinowitz condition.

Under appropriate hypotheses we establish a precise limit theorem which shows how the spectrum of A is recovered from the sequence of eigenvalues of the n × n compressions.

Furthermore, under appropriate hypotheses, the existence of its weak solutions in low order Sobolev space H s ( R ) with 1 < s ≤ 3 2 is established.

An analytical methodology has been applied, solving the continuity, momentum and energy transport equations under appropriate hypothesis.

We will prove that, under appropriates hypotheses, the graph Σ u over M k, τ T of the function u = w Φ + v, is a surface whose mean curvature vanishes.

Furthermore, Du and Xiang [16] obtained the blow-up rate estimates under some appropriate hypotheses on initial datum.

Furthermore, we establish a blow-up solution and obtain both upper and lower bounds for the maximum blow-up time under some appropriate hypotheses.

In this section, we will discuss the blow-up solution to the problem (1.1) under some appropriate hypotheses and show Theorem 1.2.