In this work, we establish the existence of nonzero solutions for a class of quasilinear elliptic equations involving indefinite nonlinearities with exponential critical growth of Trudinger–Moser type. Our proofs rely on variational arguments in a Orlicz–Sobolev space with a version of the Trudinger–Moser inequality.

中文翻译：

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涉及不确定非线性和$$ {\ mathbb {R}} ^ N $$ RN的指数临界增长的拟线性方程

在这项工作中，我们为一类涉及不确定非线性且具有Trudinger-Moser型指数增长的不确定非线性椭圆方程建立非零解的存在性。我们的证明依赖于带有Trudinger-Moser不等式的Orlicz-Sobolev空间中的变分参数。