We give sufficient conditions for the existence of weak solutions to quasilinear elliptic Dirichlet problem driven by the A-Laplace operator in a bounded domain Ω. The techniques, based on a variant of the symmetric mountain pass theorem, exploit variational methods. We also provide information about the asymptotic behavior of the solutions as a suitable parameter goes to 0+. In this case, we point out the existence of a blow-up phenomenon. The analysis developed in this paper extends and complements various qualitative and asymptotic properties for some cases described by homogeneous differential operators.

中文翻译：

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参数和非参数A-拉普拉斯问题：解的存在性和渐近分析

我们为有界Ω中的A-Laplace算子驱动的拟线性椭圆形Dirichlet问题的弱解的存在提供了充分的条件。这些技术基于对称山路定理的一种变体，采用了变分方法。当合适的参数变为0+时，我们还提供有关解的渐近行为的信息。在这种情况下，我们指出存在爆炸现象。本文开发的分析针对由齐次微分算子描述的某些情况扩展并补充了各种定性和渐近性质。