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Nonlinear multiparameter eigenvalue problems on general level sets
Nonlinear Analysis: Theory, Methods & Applications, 1997The author considers the following nonlinear multiparameter problem \[ u''(x)+ \sum^n_{k=1} \mu_kf_k \bigl(u(x)\bigr) =\lambda g\bigl(u(x) \bigr),\;u(x)>0,\;x\in I=(0,1) \tag{1} \] \[ u(0)= u(1)=0, \] where \(\mu= (\mu_1,\mu_2, \dots, \mu_n) \in \mathbb{R}^n_+\) \((\mathbb{R}_+: =(0, \infty))\), \(\lambda\in \mathbb{R}_+\) are parameters.
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Variational methods for nonlinear multiparameter elliptic eigenvalue problems
Nonlinearity, 1997Summary: We consider the following nonlinear multiparameter problem \[ u''(r)+ {N-1 \over r} u'(r)+ \sum^n_{k=1} \mu_k u(r)^{p_k} =\lambda u(r ...
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A Numerical Technique for Multiparameter Eigenvalue Problems
IMA Journal of Numerical Analysis, 1982Browne, Patrick J., Sleeman, B. D.
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Subspace method for multiparameter‐eigenvalue problems based on tensor‐train representations
Numerical Linear Algebra With Applications, 2022Koen Ruymbeek +2 more
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Method of Y-Mappings for Study of Multiparameter Nonlinear Eigenvalue Problems
Computational Mathematics and Mathematical Physics, 2022Yury G Smirnov
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A Homotopy Method for Finding All Solutions of a Multiparameter Eigenvalue Problem
SIAM Journal on Matrix Analysis and Applications, 2016Bo Dong, Bo Yu
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Generalized simple eigenvalues and bifurcation for a linked multiparameter eigenvalue problem
1996The bifurcation problem for the nonlinear multiparameter system of equations \[ L_i(\lambda)x_i= F(\lambda, x_1,\dots, x_m); \] \[ L_i(\lambda)= A_i- \sum^n_{j= 1}\lambda_j B_{ij},\quad i=1,\dots, m,\quad m\leq n \] (\(A_i\), \(B_{ij}\) are bounded selfadjoint operators on Hilbert spaces \(H_i\), \(i= 1,\dots,m\); \(\lambda_j\), \(j= 1,\dots,n\), are ...
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