Dirichlet (p,q)-equations with gradient dependent and locally defined reaction
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We consider a Dirichlet (p,q)-equation, with a gradient dependent reaction which is only locally defined. Using truncations, theory of nonlinear operators of monotone type, and fixed point theory (the Leray-Schauder Alternative Theorem), we show the existence of a positive smooth solution.
CitationLiu, Z., & Papageorgiou, N. S. (2021). Dirichlet (p,q)-equations with gradient dependent and locally defined reaction. Electronic Journal of Differential Equations, 2021(34), pp. 1-8.
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