Eigenvalues and the One-Dimensional p-Laplacian
نویسندگان
چکیده
منابع مشابه
LOWER BOUNDS FOR EIGENVALUES OF THE ONE-DIMENSIONAL p-LAPLACIAN
We also prove that the lower bound is sharp. Eigenvalue problems for quasilinear operators of p-Laplace type like (1.1) have received considerable attention in the last years (see, e.g., [1, 2, 3, 5, 8, 13]). The asymptotic behavior of eigenvalues was obtained in [6, 7]. Lyapunov inequalities have proved to be useful tools in the study of qualitative nature of solutions of ordinary linear diffe...
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and Applied Analysis 3 and using 1.9 we have ( tanpt )′ 1 − sinpt ( cospt )′ cospt 1 ∣ ∣tanpt ∣ ∣. 1.10 Like for p 2, tanpt > t for t ∈ 0, πp/2 and tanpt < t for t ∈ −πp/2, 0 , which is equivalent to ∣ ∣sinp ∣ ∣p > tΦ ( sinpt ) cospt 1.11 for t ∈ −πp/2, πp/2 , t / 0. A similar formula to 1.10 for cotp is related to the Riccati equation associated with 1.1 . Namely, if x t / 0 is a solution of 1...
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In this paper we will use variational methods and limiting approaches to give a complete solution to the maximization problems of the Dirichlet/Neumann eigenvalues of the one-dimensional p-Laplacian with integrable potentials of fixed L 1-norm.
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In this paper, we will use the variational method and limiting approach to solve the minimization problems of the Dirichlet/Neumann eigenvalues of the one-dimensional p-Laplacian when the L1 norm of integrable potentials is given. Combining with the results for the corresponding maximization problems, we have obtained the explicit results for these eigenvalues.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2002
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7742