Sentence examples for by variational methods can from inspiring English sources

For the case of bounded domain, some interesting studies by variational methods can be found in [6 14] for equation (1.4) with several growth conditions on f.

By variational methods, we can find the range of controlled parameters to ensure the existence of solutions for this type of differential model when nonlinearity f is p-suplinear growth or p-sublinear growth.

Many excellent results were obtained by variational methods [1 11].

In [21], the existence criteria of radial solutions are established under different conditions by variational methods.

The existence and multiplicity results of positive solutions are obtained by variational methods.

In [23], in the asymptotically periodic case, a nontrivial solution is obtained by variational methods.

By variational methods we consider a p-biharmonic equation with nonlocal term on unbounded domain.

For, and for,, such transformed problem was solved by variational methods in [7, 8], respectively.

Solutions are found by variational methods via an abstract perturbation result.

It seems difficult to consider the case by variational method.

The following equation is obtained by variational method using wave functions χ z): (26).