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In both cases, the existence of a solution is guaranteed from a monotone iterative technique.
The Beltrami equation is obtained using Harmonic map theory, and therefore the existence and uniqueness of a solution is guaranteed.
The existence of such a solution is guaranteed by standard results on deterministic equations (cf. [[23], Sect.
The existence of a solution is guaranteed via the method of sub- and supersolution if, among other assumptions, the functions a and b considered are C 1 sign-changing functions that may be negative near the boundary and the positive nonlinearities f and g are supposed to be C 1 and nondecreasing.
This corresponds to the Poisson equation, for which a unique solution is guaranteed for a boundary valueproblem.
The existence of a positive solution is guaranteed for large λ by applying the sub-supersolution method.
From Proposition 4, we conclude that a sparse solution is guaranteed via Algorithm 1 if the transpose of B satisfies the RSP.
The paper [5] deals with problem (P) in the particular case p = 2 and a positive solution is guaranteed by applying the sub- and supersolution method and Schauder's fixed point theorem.
The main advantage of the method comes from the fact that an integer solution is guaranteed.
Hence a first-best solution is guaranteed without moral hazard issue.
A global optimal solution is guaranteed.
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