This paper introduces a rational function preconditioner for linear systems with indefinite sparse matrices A. By resorting to rational functions of A, the algorithm decomposes the spectrum of A into two disjoint regions and approximates the restriction of A−1 on these regions separately. We show a systematic way to construct these rational functions so that they can be applied stably and inexp...

In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for an indefinite semilinear elliptic system ðEk;lÞ involving critical exponents and sign-changing weight functions. Using Nehari manifold, the system is proved to have at least two nontrivial nonnegative solutions when the pair of the parameters ðk;lÞ belongs to a certain subset of R. 20...

We are interested in the asymptotic analysis of singular solutions with blowup boundary for a class of quasilinear logistic equations with indefinite potential. Under natural assumptions, we study the competition between the growth of the variable weight and the behaviour of the nonlinear term, in order to establish the blow-up rate of the positive solution. The proofs combine the Karamata regu...

We establish the existence of nontrivial solutions for an elliptic system which is resonant both at the origin and at infinity. The resonance is given by an eigenvalue problem with indefinite weight, and the nonlinear term is permitted to be unbounded. Also, we consider the case where the resonance at infinity and at the origin can occur with different weights. Our main tool is the computation ...

Certain properties of indefinite pronouns have received considerable attention in the literature. For instance, negative polarity indefinites such as English any constitute the focus of the bulk of the literature on negative polarity items, the fact notwithstanding that Klima in his seminal 1964 paper did not fail to show that members of other syntactic and semantic categories may be restricted...

We consider a singular Sturm-Liouville expression with the indefinite weight sgnx. To this expression there is naturally a self-adjoint operator in some Krein space associated. We characterize the local definitizability of this operator in a neighbourhood of ∞. Moreover, in this situation, the point ∞ is a regular critical point. We construct an operator A = (sgnx)(−d2/dx2 + q) with non-real sp...

We obtain a formula relating the Fourier coefficients of a modular form of half-integral weight (that is constructed as a theta lift from an indefinite quaternion algebra B over Q) to the special values of L-functions. This formula has applications to proving the nonvanishing of a certain explicit theta lift and to an explicit version of the Rallis inner product formula for the dual pair (S̃L2, ...

In this paper, we study the spectral theory for nonlocal dispersal operators with time periodic indefinite weight functions subject to Dirichlet type, Neumann type and spatial periodic type boundary conditions. We first obtain necessary and sufficient conditions for the existence of a unique positive principal spectrum point for such operators. We then investigate upper bounds of principal spec...

In this paper, using sub-supersolution argument, we prove an existence result on positive solution for an ecological model under certain conditions. It also describes the dynamics of the fish population with natural predation and constant yield harvesting. The assumptions are that the ecosystem is spatially homogeneous and the herbivore density is a constant which are valid assumptions for mana...

The numerical range of a quadratic operator acting on an indefinite inner product space is shown to have a hyperbolical shape. This result is extended to different kinds of indefinite numerical ranges, namely, indefinite higher rank numerical ranges and indefinite Davis-Wielandt shells.