【摘要】 <正> §1.引言燃烧放热反应的定常问题可用如下的带两个参数的非线性椭圆型方程的边值问题来描写更多还原

【Abstract】 This paper is concerned with the steady problems in the theory of the thermal ignition. They can be described by a kind of boundary value problems of nonlinear elliptic differential equations with two parameters λ, μ. We prove that the solutions of the nonlinear EBVP always exist for any λ, μ>0. The uniqueness of the solution of the nonlinear EBVP is given for the case μ<μ⁰ where μ₀ is the only positive root of the equation λ_x（m）μ²—M₀exp （2/μ）=0. If μ is small, the uniqueness can only be proved for the cases of small λ or large λ. Meanwhile the existence of the fold points （λ^*, μ（λ^*）） on the solution family u（λ） of the nonlinear EBVP for the fixed μ<μ^*, where μ⁰=min （2/1,（?）） is proved. Also we prove that at least three solution of the nonlinear EBVP exist for some region of λ if μ<μ^*. All above properties of the solutions of the nonlinear EBVP are suggested by the numerical results. Finally we discuss the stability of the multiple solutions.更多还原