Sentence examples for indefinite problem from inspiring English sources

Thus, in this paper, we only consider the non-resonant strongly indefinite problem.

The idea originates from Drabek et al. [25], where the authors study an indefinite problem in the classical Euclidean space (mathbb{R}^{N}), and some refinement from Chen [24], where the author studied an indefinite problem with singular term.

Our approach is based on an application of a variant generalized weak linking strongly indefinite problem developed by Schechter and Zou [21]; also see Chen and Ma [22].

(10) Our approach is based on an application of a variant and generalized weak linking theorem for strongly indefinite problem developed by Schechter and Zou [16], also see Chen and Ma [11].

Very recently, López-Gómez, Omari, Rivetti [46, 47] studied a class of quasilinear indefinite problem textstylebegin{cases} - frac{u'}{sqrt{1+u^{prime2}}})'=lambda a(t)f u),quad 0< t< 1, u'(0)=u'(1)=0, end{cases} (1.8) where (lambdainmathrm{R}) is a parameter, (ain L^{1}[0,1]) changes sign.

Comparing with other related indefinite problems [29 32], the main features of this paper are as follows.

For other results on indefinite problems, we refer the reader to Refs. [48 51] and the references cited therein.

The generality of our result enables us to apply not only any known preconditioners designed for symmetric positive definite problems, but also many other preconditioners based on original operator to nonsymmetric and indefinite problems without losing optimality.

Moreover, a class of indefinite problems have attracted the attention of Ma and Han [38], López-Gómez and Tellini [39], Boscaggin and Zanolin [40, 41], Sovrano and Zanolin [42], Bravo and Torres [43], Wang and An [44], and Yao [45].

In this paper an iterative method of the multiple level type is proposed for solving systems of algebraic equations which arise from thep-version of the finite element analysis applied to indefinite problems.

Very recently, López-Gómez, Omari, and Rivetti [37, 38] studied a class of quasilinear indefinite problems textstylebegin{cases} - (frac{u'}{sqrt{1+u^{prime2}}} )'=lambda a(x f u), u'(0)=u'(1)=0, end{cases} where (lambdainmathcal{R}) is a parameter, (ain L^{1}[0,1]) changes sign.