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Blow up for some nonlinear parabolic problems with convection under dynamical boundary conditions
On the existence of fixed-sign solutions for a system of generalized right focal problems with deviating arguments
| 1. | School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore |
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$u^(''')_ i (t) = f_i(t, u_1(\phi_ 1(t)), u_2(\phi_ 2(t)), · · · , u_n(\phi_ n(t))), t \in [a, b]$ $u_i(a) = u^'_i(z_i) = 0$, \gamma_i u_i(b) + \delta_iu^('')_i (b) = 0$
where $i$ = 1, 2, · · · , $n$, $1/2 (a + b) < z_i < b, \gamma_i > 0$, and $\phi_ i$ are deviating arguments. By using some fixed point theorems, we establish the existence of one or more fixed-sign solutions $u = (u_1, u_2, · · · , u_n)$ for the system, i.e., for each 1 $<=$ $i$ $<=$ $n$, $\theta_iui(t) >= 0$ for $t \in [a, b]$, where $\theta_i \in$ {1,−1} is fixed. An example is also presented to illustrate the results obtained.
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