Abstract For studying the evolution of transverse deflection an extensible beam derived from connection mechanics, we investigate initial boundary value problem nonlinear equation with linear strong damping term, weak and source term. The key idea our analysis is to describe invariant manifold via Nehari manifold. To establish results global well-posedness solution, consider at three different ...

In this paper, the nonexistence of tight spherical designs is shown in some cases left open to date. Tight spherical 5-designs may exist in dimension n = (2m + 1)2 − 2, and the existence is known only for m = 1, 2. In the paper, the existence is ruled out under a certain arithmetic condition on the integer m, satisfied by infinitely many values of m, including m = 4. Also, nonexistence is shown...

In this article, we investigate the existence, uniqueness, nonexistence, and regularity of weak solutions to nonlinear fractional elliptic problem type (P) (see below) involving singular nonlinearity weights in smooth bounded domain. We prove existence solution $$W_{loc}^{s,p}(\Omega )$$ via approximation method. Establishing a new comparison principle independent interest, uniqueness for $$0 \...

Semilinear elliptic equations which give rise to solutions blowing up at the boundary are perturbed by a Hardy potential μ/δ(x, ∂Ω). The size of this potential effects the existence of a certain type of solutions (large solutions): if μ is too small, then no large solution exists. The presence of the Hardy potential requires a new definition of large solutions, following the pattern of the asso...

In this paper we consider the nonlinearly damped semilinear Petrovsky equation utt + 2u+ aut ut m−2 = bu u p−2 in a bounded domain, where a b > 0. We prove the existence of a local weak solution and show that this solution blows up in finite time if p > m and the energy is negative. We also show that the solution is global if m ≥ p.  2002 Elsevier Science

<p style='text-indent:20px;'>In this paper, we study the initial boundary value problem of visco-elastic dynamical system with nonlinear source term in control system. By variational arguments and an improved convexity method, prove global nonexistence solution, also give a sharp condition for existence nonexistence.</p>

We investigate the existence and nonexistence of positive solutions of a system of secondorder nonlinear ordinary differential equations, subject to integral boundary conditions. 2010 AMS Subject Classification: 34B10, 34B18.

We consider the (n−1, 1) conjugate boundary value problem. Some upper estimates to positive solutions for the problem are obtained. We also establish some explicit sufficient conditions for the existence and nonexistence of positive solutions of the problem.

In this paper, two second order half-linear difference equations are considered. By establishing their connections with a standard half-linear difference equation, we are able to obtain sufficient conditions for existence and nonexistence of eventually positive solutions.