Under general hypotheses, we prove the existence of a nontrivial solution for the equation Lu = N(u), where u belongs to a Hilbert space H , L is an invertible continuous selfadjoint operator, and N is superlinear. We are particularly interested in the case where L is strongly indefinite and N is not compact. We apply the result to the Choquard-Pekar equation -Au(x)+p(x)u(x) = u(x) f U <'y\ dy,...

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.

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.

‎We prove that there do not exist totally contact umbilical‎ ‎proper slant lightlike submanifolds of indefinite Sasakian manifolds other than totally contact geodesic‎ ‎proper slant lightlike submanifolds‎. ‎We also prove that there do‎ ‎not exist totally contact umbilical proper slant lightlike‎ ‎submanifolds of indefinite Sasakian space forms‎.

An indefinite weight eigenvalue problem characterizing the threshold condition for extinction of a population based on the single-species diffusive logistic model in a spatially heterogeneous environment is analyzed in a bounded two-dimensional domain with no-flux boundary conditions. In this eigenvalue problem, the spatial heterogeneity of the environment is reflected in the growth rate functi...

Inspired by the classical Poincaré criterion about instability of orientation preserving minimizing closed geodesics on surfaces, we investigate relation intertwining and variational properties periodic solutions a non-autonomous Lagrangian finite dimensional Riemannian manifold. We establish general for priori detecting linear orbit manifold (maybe not Legendre convex) simply looking at parity...

We present a compared analysis of some properties of indefinite almost S-manifolds and indefinite S-manifolds. We give some characterizations in terms of the Levi-Civita connection and of the characteristic vector fields. We study the sectional and φ-sectional curvature of indefinite almost S-manifolds and state an expression of the curvature tensor field for the indefinite S-space forms. We an...

The subject of this paper is the semantics of propositional disjunctive logic programs and indefinite deductive data bases. The concept of the indefinite model of a disjunctive logic program is introduced. The algorithm of computing the indefinite model and an algorithm of evaluation of clauses in the indefinite model, both using a parallel positive variant of resolution, are presented. The eva...

In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As application, the Hahn-Banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

‎we prove that there do not exist totally contact umbilical‎ ‎proper slant lightlike submanifolds of indefinite sasakian manifolds other than totally contact geodesic‎ ‎proper slant lightlike submanifolds‎. ‎we also prove that there do‎ ‎not exist totally contact umbilical proper slant lightlike‎ ‎submanifolds of indefinite sasakian space forms‎.