Global bifurcation and local multiplicity results for elliptic equations with singular nonlinearity of super exponential growth in $\mathbb{R}^2$
Global bifurcation and local multiplicity results for elliptic equations with singular nonlinearity of super exponential growth in $\mathbb{R}^2$
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$mathbb{R}^2$ 中具有超指数增长奇异非线性的椭圆方程的全局分岔和局部重数结果
DOI：
10.57262/ade/1355703090
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发表时间：
2012
影响因子：
1.4
通讯作者：
K. Saoudi
中科院分区：
文献类型：
--
作者：
R. Dhanya;J. Giacomoni;S. Prashanth;K. Saoudi
本文研究了有界光滑区域Ω <$R2中指数型增长的奇异椭圆问题的解：
− u = λ（u−δ + h（u）eu），单位为Ω，
（Pλ）{ u > 0 in Ω，u| Ω = 0。
这里，1 ≤ α ≤ 2，0 < δ < 3，λ ≥ 0，假设h（t）是t → ∞时的一个光滑α“扰动”（参见下面的（H1）−（H2）），我们证明了（Pλ）的解的无界连通分支的存在性，该分支源自λ = 0的平凡解。在径向情况下（即，当Ω = B_1且u是径向对称的），我们详细研究了解的分支在无穷远处接近渐近分歧点时的爆破/收敛性.在α = 2的临界情形下，我们用相应的分歧图和大解沿着的渐近分布解释了多重性结果
无穷远处的分支。
In this paper, we study the solutions to the following singular elliptic problem of exponential type growth posed in a bounded smooth domain Ω ⊂ R2 :
−∆u = λ(u−δ + h(u)eu ) in Ω,
(Pλ) { u > 0 in Ω, u|∂Ω = 0.
Here, 1 ≤ α ≤ 2, 0 < δ < 3, λ ≥ 0 and h(t) is assumed to be a smooth α “perturbation” of et as t → ∞ (see (H1) − (H2) below).We show the existence of an unbounded connected branch of solutions to (Pλ ) emanating from the trivial solution at λ = 0. In the radial case (i.e., when Ω = B1 and u is radially symmetric) we make a detailed study of the blow-up/convergence of the solution branch as it approaches the asymptotic bifurcation point at infinity. In the critical case α = 2, we interpret the multiplicity results in terms of the corresponding bifurcation diagrams and the asymptotic profile of large solutions along
the branch at infinity.
影响因子：
1.4
作者：
K. Nagasaki;Takashi Suzuki
通讯作者：
K. Nagasaki;Takashi Suzuki