We study the family of blowup solutions to semilinear elliptic equations in two-space dimensions with exponentially-dominated nonnegative nonlinearities. Such a family admits an exclusion of the boundary blowup, finiteness of blowup points, and pattern formation. Then, Hamiltonian control of the location of blowup points, residual vanishing, and mass quantization arise under the estimate from below of the nonlinearity. Finally, if the principal growth rate of nonlinearity is exactly exponential and the residual part has a gap relative to this term, there is a locally uniform estimate of the solution which ensures its asymptotic non-degeneracy.

中文翻译：

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具有指数支配非线性的二维椭圆方程解的局部和全局行为

我们研究了具有指数支配的非负非线性的二维半线性椭圆方程的放大解系列。这样的族允许排除边界膨胀、膨胀点的有限性和模式形成。然后，在非线性下方的估计下，出现了对爆破点位置、残差消失和质量量化的哈密顿控制。最后，如果非线性的主要增长率恰好是指数的，而残差部分相对于该项有一个间隙，则解的局部均匀估计可以确保其渐近非简并性。