‎in this paper‎, ‎we formulate the sixth-order boundary value problem as fredholm integral equation by finding green's function and obtain the sufficient conditions for existence and multiplicity of positive solution for this problem‎. ‎also nonexistence results are obtained‎. ‎an example is given to illustrate the results of paper‎.

Completely transitive codes were introduced by P. Solé as a special case of binary linear completely regular codes. The existence of such codes is closely related to the existence of certain permutation groups. The nonexistence of highly transitive permutation groups allows us to prove the nonexistence of completely transitive codes with error-correcting capability greater than 4.

The existence, nonexistence and multiplicity of positive radially symmetric solutions to a class of Schrödinger–Poisson type systems with critical nonlocal term are studied with variational methods. The existence of both the ground state solution and mountain pass type solutions are proved. It is shown that the parameter ranges of existence and nonexistence of positive solutions for the critica...

This paper deals with the global existence and the global nonexistence of a doubly nonlinear parabolic system coupled via both nonlinear reaction terms and nonlinear boundary flux. The authors first establish a weak comparison principle, then by constructing various upper and lower solutions, some appropriate conditions for global existence and global nonexistence of solutions are determined re...

In the present paper, we study the existence of descriptive patterns, i. e. patterns that cover all words in a given set through morphisms and that are optimal in terms of revealing commonalities of these words. Our main result shows that if patterns may be mapped onto words by arbitrary morphisms, then there exist infinite sets of words that do not have a descriptive pattern. This answers a qu...

In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinitedimensional Banach space that is very different from—and considerably shorter than—the one recently given by Bermúdez, Bonilla and Martinón. We also show the existence of a strongly dense family of topologically mixing operators on every separable infinite...

In this paper we are studying the existence of positive entire large solutions for the problem ∆u = p1(x)u α + p2(x)u f(u) in R , N ≥ 3. Moreover, we are interested in the relation between the existence or nonexistence of such solutions for the above problem and the existence or nonexistence of such solutions for the problems ∆u = p1(x)u α and ∆u = p2(x)u f(u).

this paper is concerned with a 2nth-order p-laplacian difference equation. by using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for neumann boundary value problem and give some new results. results obtained successfully generalize and complement the existing ones.