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.
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.
Moreover, as p is close to 2, we get the fourth nontrivial solution under appropriate hypotheses, where f x,u) satisfies Ambrosetti Rabinowitz condition.
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.
In this paper, we study ( p ( x ), q ( x ) ) -biharmonic systems with Navier boundary condition on a bounded domain and obtain three solutions under appropriate hypotheses.
We prove that, under appropriate hypotheses, such a solution set is dense and codense in the solution set of a system with a convexified right-hand side ('bang-bang' principle).
Moreover, under appropriate hypotheses, the criteria to identify the simultaneous and nonsimultaneous quenching are found, and the four kinds of quenching rates for different nonlinear exponent regions are given.
Furthermore, under appropriate hypotheses and by applying Morse theory coupled with local linking arguments, Zhao et al. [36] obtained the existence of at least one nontrivial solution for problem (1.2), in the case (lambda=mu=1).
