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The bounded and positive solutions of quasilinear elliptic differential equations in unbounded domains. (Chinese. English summary) Zbl 0875.35032

Summary: Existence and uniqueness of the bounded and positive solutions of Dirichlet problems for quasilinear elliptic differential equations of non-divergence type in unbounded domains are proved. Here, we mainly use the method of super-functions and sub-functions and a local approach. Under certain assumptions we present sufficient and necessary conditions for the existence of super-functions and sub-functions.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35A35 Theoretical approximation in context of PDEs
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