We complement the recently introduced classes of lower and upper semilinear copulas by two new classes, called vertical and horizontal semilinear copulas, and characterize the corresponding class of diagonals. The new copulas are in essence asymmetric, with maximum asymmetry given by 1/16. The only symmetric members turn out to be also lower and upper semilinear copulas, namely convex sums of Π...

We consider a diffusive p–logistic equation in the whole of R with absorption and an indefinite weight. Using variational and truncation techniques we prove a bifurcation theorem and describe completely the bifurcation point. In the semilinear case p = 2, under an additional hypothesis on the absorption term, we show that the positive solution is unique.

In this paper we consider the nonlinearly damped semilinear wave equation utt −∆u + aut |ut|m−2 = bu|u|p−2 associated with initial and Dirichlet boundary conditions. We prove that any strong solution, with negative initial energy, blows up in finite time if p > m. This result improves an earlier one in [2].

A semilinear relation S ⊆ Qn is max-closed if it is preserved by taking the componentwise maximum. The constraint satisfaction problem for max-closed semilinear constraints is at least as hard as determining the winner in Mean Payoff Games, a notorious problem of open computational complexity. Mean Payoff Games are known to be in NP∩ co-NP, which is not known for max-closed semilinear constrain...

In this paper, we partially answer open questions about the convergence of overlapping Schwarz methods. We prove that overlapping Schwarz methods with Dirichlet transmission conditions for semilinear elliptic and parabolic equations always converge, while overlapping Schwarz methods with Robin transmission conditions only converge for semilinear parabolic equations, but the convergence is not g...

Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In ...

Solutions of the semilinear wave equation are found numerically in three spatial dimensions with no assumed symmetry using distributed adaptive mesh refinement. The threshold of singularity formation is studied for the two cases in which the exponent of the nonlinear term is either p = 5 or p = 7. Near the threshold of singularity formation, numerical solutions suggest an approach to self-simil...

In this paper, we present a detailed study of class sixth-order semilinear PDEs: existence, regularity and uniqueness. The uniqueness results are consequence maximum principle called the P-function method.

A semilinear relation is a finite union of finite intersections of open and closed half-spaces over, for instance, the reals, the rationals, or the integers. Semilinear relations have been studied in connection with algebraic geometry, automata theory, and spatiotemporal reasoning. We consider semilinear relations over the rationals and the reals. Under this assumption, the computational comple...

1 Institute of Mathematics and Computer Science Academy of Sciences of Moldova Str. Academiei 5, Chişinău, MD 2028, Moldova E-mail: [email protected] 2 Dipartimento di Informatica, Sistemistica e Comunicazione Università degli Studi di Milano-Bicocca Viale Sarca 336/14, 20126 Milano, Italy E-mail: {o.belingheri@campus,porreca@disco,zandron@disco}.unimib.it 3 Faculty of Informatics, TU Wien Favorit...