We study the existence of positive supersolutions of nonlocal equations of type \((-\Delta)^{s} u + |\Delta u|^{q} = \lambda f(u)\) posed in exterior domains where the datum f can be comparable with \(u^p\) near the origin. We prove that the existence of bounded supersolutions depends on the values of p, q and s.

中文翻译：

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具有梯度项的非局部方程超解的存在性研究

我们研究存在于基准面外域中的\（（-\ Delta）^ {s} u + | \ Delta u | ^ {q} = \ lambda f（u）\）类型的非局部方程的正超解的存在f可以与原点附近的\（u ^ p \）相媲美。我们证明有界超解的存在取决于p，q和s的值。