The Experts below are selected from a list of 8211 Experts worldwide ranked by ideXlab platform
Su Jiabao - One of the best experts on this subject based on the ideXlab platform.
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semilinear elliptic resonant problems at Higher Eigenvalue with unbounded nonlinear terms
Acta Mathematica Sinica, 1998Co-Authors: Su JiabaoAbstract:In this paper we study the existence of nontrivial solutions of a class of asymptotically linear elliptic resonant problems at Higher Eigenvalues with the nonlinear term which may be unbounded by making use of the Morse theory for aC2-function at both isolated critical point and infinity.
Rafael D Benguria - One of the best experts on this subject based on the ideXlab platform.
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isoperimetric bounds for Higher Eigenvalue ratios for the n dimensional fixed membrane problem
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 1993Co-Authors: Mark S Ashbaugh, Rafael D BenguriaAbstract:We give several results which extend our recent proof of the Payne-Polya–Weinberger conjecture to ratios of Higher Eigenvalues. In particular, we show that for a bounded domain Ω⊂ℝn the Eigenvalues of its Dirichlet Laplacian obey where λm denotes the mth Eigenvalue and jp,k denotes the kth positive zero of the Bessel function Jp(x). Certain extensions of this result are given, the most general being the bound where k≧2 and l(m) denotes the number of nodal domains of an mth eigenfunction. Our results imply certain further conjectures of Payne, Polya, and Weinberger concerning λ3/λ2 and λ4/λ3. In addition, we find a resonably good bound on λ4/λ1. We also briefly discuss extensions to Schrodinger operators and other elliptic Eigenvalue problems.
Yintzer Shih - One of the best experts on this subject based on the ideXlab platform.
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tailored finite point methods for solving singularly perturbed Eigenvalue problems with Higher Eigenvalues
Journal of Scientific Computing, 2017Co-Authors: Houde Han, Yintzer Shih, Dongsheng YinAbstract:We study tailored finite point methods (TFPM) for solving the singularly perturbed Eigenvalue (SPE) problems. We first provide an asymptotic analysis for the eigenpairs and show that for some special potential functions when $$\varepsilon $$ approaches to zero the square of eigenfunction converges to a Dirac delta function weakly, and the Eigenvalue converges to the minimum value of the potential function. For computing the eigenfunction with Higher Eigenvalue we propose two variants of TFPM for one-dimensional SPE problems and a nonlinear least square TFPM for two-dimensional problems. The eigenfunction with Higher Eigenvalue can be easily computed on a related coarse mesh on numerical tests, and suggests that the proposed schemes are accurate and efficient for the SPE problems.
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tailored finite point methods for Higher eigenpairs of singular perturbed Eigenvalue problems
IMACS2016, 2016Co-Authors: Yintzer Shih, Houde Han, Tongsheng YingAbstract:We study tailored finite point methods (TFPM) for solving the singular perturbed Eigenvalue(SPE) problems. We first provide an asymptotic analysis for the eigenpairs and show thatfor some special potential functions when " approaches to zero the square of eigenfunctionconverges to a Dirac delta function weakly, and the Eigenvalue converges to the minimum valueof the potential function. For computing the eigenfunction with Higher Eigenvalue we proposetwo variants of TFPM for one-dimensional SPE problems and a nonlinear least square TFPM(LSTFPM) for two-dimensional problems. The eigenfunction with Higher Eigenvalue can beeasily computed on a related coarse mesh on numerical tests, and suggests that the proposedschemes are accurate and efficient for the SPE problems.
Houde Han - One of the best experts on this subject based on the ideXlab platform.
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tailored finite point methods for solving singularly perturbed Eigenvalue problems with Higher Eigenvalues
Journal of Scientific Computing, 2017Co-Authors: Houde Han, Yintzer Shih, Dongsheng YinAbstract:We study tailored finite point methods (TFPM) for solving the singularly perturbed Eigenvalue (SPE) problems. We first provide an asymptotic analysis for the eigenpairs and show that for some special potential functions when $$\varepsilon $$ approaches to zero the square of eigenfunction converges to a Dirac delta function weakly, and the Eigenvalue converges to the minimum value of the potential function. For computing the eigenfunction with Higher Eigenvalue we propose two variants of TFPM for one-dimensional SPE problems and a nonlinear least square TFPM for two-dimensional problems. The eigenfunction with Higher Eigenvalue can be easily computed on a related coarse mesh on numerical tests, and suggests that the proposed schemes are accurate and efficient for the SPE problems.
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tailored finite point methods for Higher eigenpairs of singular perturbed Eigenvalue problems
IMACS2016, 2016Co-Authors: Yintzer Shih, Houde Han, Tongsheng YingAbstract:We study tailored finite point methods (TFPM) for solving the singular perturbed Eigenvalue(SPE) problems. We first provide an asymptotic analysis for the eigenpairs and show thatfor some special potential functions when " approaches to zero the square of eigenfunctionconverges to a Dirac delta function weakly, and the Eigenvalue converges to the minimum valueof the potential function. For computing the eigenfunction with Higher Eigenvalue we proposetwo variants of TFPM for one-dimensional SPE problems and a nonlinear least square TFPM(LSTFPM) for two-dimensional problems. The eigenfunction with Higher Eigenvalue can beeasily computed on a related coarse mesh on numerical tests, and suggests that the proposedschemes are accurate and efficient for the SPE problems.
Dongsheng Yin - One of the best experts on this subject based on the ideXlab platform.
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tailored finite point methods for solving singularly perturbed Eigenvalue problems with Higher Eigenvalues
Journal of Scientific Computing, 2017Co-Authors: Houde Han, Yintzer Shih, Dongsheng YinAbstract:We study tailored finite point methods (TFPM) for solving the singularly perturbed Eigenvalue (SPE) problems. We first provide an asymptotic analysis for the eigenpairs and show that for some special potential functions when $$\varepsilon $$ approaches to zero the square of eigenfunction converges to a Dirac delta function weakly, and the Eigenvalue converges to the minimum value of the potential function. For computing the eigenfunction with Higher Eigenvalue we propose two variants of TFPM for one-dimensional SPE problems and a nonlinear least square TFPM for two-dimensional problems. The eigenfunction with Higher Eigenvalue can be easily computed on a related coarse mesh on numerical tests, and suggests that the proposed schemes are accurate and efficient for the SPE problems.