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arXiv · 1901.03176

Existence of solutions of semilinear systems with gradient dependence via eigenvalue criteria

Filomena Cianciaruso
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Abstract

In this paper new criteria are established for the existence of positive radial solutions of a semilinear elliptic system depending on the gradient. These criteria are determined by some relationships between the upper and lower bounds on suitable stripes of $\mathbb R^n$ of the nonlinearities of the system and the principal characteristic values of some associated linear Hammerstein integral operators. Moreover, using smoothing tools, the totality of the involved cone is established.

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Filomena Cianciaruso. 2019-01-10. Existence of solutions of semilinear systems with gradient dependence via eigenvalue criteria. https://arxiv.org/abs/1901.03176

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