This dissertation is to discuss the initial-boundary value problem under the third nonlinear boundary condition for a kind of nonlinear evolution equations. To apply the maximum value theory and convex functional method£it is proved that the blowing up of solution in the definite time under some assumed conditions. The conclusion popularizes the results of references [Zhongwei Zha(2003)-Zhongwe...

The evolution of a magnetoelastic material is described by a nonlinear hyperbolic-parabolic system. We introduce a simplified but nontrivial model and prove the existence of a unique solution to the corresponding initial boundary value problem. On a hyperbolic-parabolic system arising in magnetoelasticity M. Chipot∗ I. Shafrir† V. Valente ‡ G. Vergara Caffarelli§ November 6, 2007 keywords: Magn...

in this work, by employing the krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime...

An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth...