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Large solutions for non-divergence structure equations with singular lower order terms. (English) Zbl 1359.35070

Summary: In this paper we investigate infinite boundary value problems associated with the semilinear PDE \(L u = k(x) f(u)\) on a bounded smooth domain \(\Omega \subset \mathbb{R}^n\), where \(L\) is a non-divergence structure, uniformly elliptic operator with singular lower order terms. The weight \(k\) is a continuous non-negative function and \(f\) is a continuous nondecreasing function that satisfies the Keller-Osserman condition. We study a sufficient condition on \(k\) that ensures existence of a large solution \(u\). In case the lower order terms of \(L\) are bounded, under further assumptions on \(f\) and \(k\) we establish asymptotic bounds of solutions \(u\) near the boundary \(\partial\Omega\) and, as a consequence, a uniqueness result.

MSC:

35J61 Semilinear elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
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