| Abstract: |
| The Gerand boundary value problem is from a solid fuel ignition model in thermal combustion theor\textbf{y: }$\left \{\begin{array}{c}\mathbf{u}^{ \prime \prime }(\mathbf{t}) +\mathbf{\lambda }\exp (\genfrac{(}{)}{}{}{\alpha u(t)}{\alpha +u(t)}) =0 ,\text{ } -1 0$ is the activation energy parameter, u(t) represents the temperature of the combustion, and the reaction term $\exp (\genfrac{(}{)}{}{}{\alpha u(t)}{\alpha +u(t)})$ comes from the temperature dependence obeying the simple Arrhenius reaction rate law in irreversible chemical reaction kinetics. We convert this problem into an integral equation by finding its Green`s function and investigate how its number of solutions, the upper and lower bounds depend on the parameters $\alpha $ and $\lambda .$ |
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