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This article is cited in 1 scientific paper (total in 1 paper)
On asymptotics of solutions to semilinear elliptic equations near the first eigenvalue of the nonperturbed problem
Ya. Sh. Il'yasov Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
The following elliptic equations with $p$-Laplacian
$$
-\Delta_pu=\lambda g(x)|u|^{p-2}u+f(x)|u|^{\gamma-2}u
$$
are considered in the entire space $\mathbb R^N$ and in the bounded domain with the Dirichlet boundary conditions. By the fibering method for the basic positive solutions of these equations, we derive the following asymptotic formula
$$
u^\lambda=(\lambda_1-\lambda)^{1/(\gamma-p)}u_1
+o\bigl((\lambda_1-\lambda)^{1/(\gamma-p)}\bigr)
$$
for $\lambda\uparrow\lambda_1$, where $\lambda_1$ is the first eigenvalue and $u_1$ is the corresponding eigenfunction of nonperturbed problem ($f=0$).
Received: 25.06.1997
Citation:
Ya. Sh. Il'yasov, “On asymptotics of solutions to semilinear elliptic equations near the first eigenvalue of the nonperturbed problem”, Mat. Zametki, 64:4 (1998), 543–548; Math. Notes, 64:4 (1998), 471–475
Linking options:
https://www.mathnet.ru/eng/mzm1428https://doi.org/10.4213/mzm1428 https://www.mathnet.ru/eng/mzm/v64/i4/p543
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Abstract page: | 401 | Full-text PDF : | 159 | References: | 31 | First page: | 1 |
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