Sentence examples for methods the existence from inspiring English sources

Since this is so it becomes at least logically possible indirectly to verify by empirical methods the existence of such realities.

By using variational methods, the existence of at least two positive solutions was obtained.

With the help of the variational methods, the existence of a non-trivial solution is obtained.

By virtue of variational methods, the existence criteria of infinitely many nontrivial high or small energy solutions are established.

With the aids of the variational methods, the existence and multiplicity of homoclinic orbits for (1.2) have been extensively investigated in many recent papers; see [2 24].

By using the least action principle and the minimax methods, the existence of periodic solutions for a class of second order Hamiltonian systems is considered.

Based on the Lyapunov Razumikhin method, the existence of a delay-dependent fault estimator is given in terms of the solvability of bilinear matrix inequalities (BMIs).

Compared with traditional hot air drying method, the existence of optimal material layer thickness is a significant phenomenon in microwave thin layer drying process.

Furthermore, by an SOS-based method the existence of the proposed controller is given in terms of the solvability of polynomial matrix inequalities (PMIs), which are formulated as SOS constraints and can be solved by the recently developed SOS solvers.

By using the variational method, the existence and multiplicity of positive solutions are obtained.

Applying the Banach contraction theorem and a modified Picard method, the existence and uniqueness of a classical solution is given.