In this paper, we study a class of nonlinear boundary value problems in R+ . By means of minimax method and the Lusternik-Schnirelman category, the criteria of the existence, multiplicity and nonexistence of positive solutions are established.

We establish conditions for existence and for nonexistence of nontrivial solutions to an elliptic system of partial differential equations. This system is of gradient type and has a nonlinearity with critical growth.

We consider the problem of the existence of uniquely partitionable planar graphs. We survey some recent results and we prove the nonexistence of uniquely (D1,D1)-partitionable planar graphs with respect to the property D1 ”to be a forest”.

In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell's nonlocality do...

As well known, the existence and nonexistence of solutions for nonlinear algebraic systems are very important since they can provide the necessary information on limiting behaviors of many dynamic systems, such as the discrete reaction-diffusion equations, the coupled map lattices, the compartmental systems, the strongly damped lattice systems, the complex dynamical networks, the discrete-time ...

The class of completely transitive codes was introduced by Solé as a proper subclass of binary linear completely regular codes. There exist completely transitive codes with error-correcting capabilities = 1 2 and 3. In a previous correspondence, Borges and Rifà proved the nonexistence of completely transitive codes with more than two codewords and error-correcting capability 4. In this correspo...