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Singular Solutions of Elliptic Equations with Iterated Exponentials
The Journal of Geometric Analysis ( IF 1.2 ) Pub Date : 2019-09-13 , DOI: 10.1007/s12220-019-00277-1 Marius Ghergu , Olivier Goubet
The Journal of Geometric Analysis ( IF 1.2 ) Pub Date : 2019-09-13 , DOI: 10.1007/s12220-019-00277-1 Marius Ghergu , Olivier Goubet
We construct positive singular solutions for the problem \(-\Delta u=\lambda \exp (e^u)\) in \(B_1\subset {\mathbb {R}}^n\) (\(n\ge 3\)), \(u=0\) on \(\partial B_1\), having a prescribed behaviour around the origin. Our study extends the one in Miyamoto (J Differ Equ 264:2684–2707, 2018) for such nonlinearities. Our approach is then carried out to elliptic equations featuring iterated exponentials.
中文翻译:
具有迭代指数的椭圆型方程的奇异解
我们构建了该问题正奇异解\( - \德尔塔U = \拉姆达\ EXP(E ^ u)的\)在\(B_1 \子集{\ mathbb {R}} ^ N \) (\(N \ GE 3 \)),\(\ partial B_1 \)上的\(u = 0 \),在原点周围具有规定的行为。对于此类非线性,我们的研究扩展了宫本的研究(J Differ Equ 264:2684-2707,2018)。然后对具有迭代指数的椭圆方程执行我们的方法。
更新日期:2019-09-13
中文翻译:
具有迭代指数的椭圆型方程的奇异解
我们构建了该问题正奇异解\( - \德尔塔U = \拉姆达\ EXP(E ^ u)的\)在\(B_1 \子集{\ mathbb {R}} ^ N \) (\(N \ GE 3 \)),\(\ partial B_1 \)上的\(u = 0 \),在原点周围具有规定的行为。对于此类非线性,我们的研究扩展了宫本的研究(J Differ Equ 264:2684-2707,2018)。然后对具有迭代指数的椭圆方程执行我们的方法。