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Multiple Solutions of Singular Perturbation Problems [PDF]
SIAM Journal on Mathematical Analysis, 1972 Under certain conditions on g(x, u) we establish the existence and asymptotic behavior for small ε > 0 of multiple asymptotic solutions of the nonlinear boundary value problem εu" + u’ - g(x,u) = 0, 0 < x < 1, u’(0) - au(0)= A ≥ 0, a > 0, u’(1) + bu(
Cohen, Donald S.
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Motion control and singular perturbation algorithms for lower limb rehabilitation robots [PDF]
Frontiers in NeuroroboticsTo better assist patients with lower limb injuries in their rehabilitation training, this paper focuses on motion control and singular perturbation algorithms and their practical applications.
Yanchun Xie +5 more
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Singular anisotropic equations with a sign-changing perturbation
Nonlinear Analysis, 2023 We consider an anisotropic Dirichlet problem driven by the variable (p, q)-Laplacian (double phase problem). In the reaction, we have the competing effects of a singular term and of a superlinear perturbation. Contrary to most of the previous papers, we
Zhenhai Liu, Nikolaos S. Papageorgiou
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The Super-Diffusive Singular Perturbation Problem
Mathematics, 2020 In this paper we study a class of singularly perturbed defined abstract Cauchy problems.
Edgardo Alvarez, Carlos Lizama
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Physics-Based Neural Network Methods for Solving Parameterized Singular Perturbation Problem
Computation, 2021 This work is devoted to the description and comparative study of some methods of mathematical modeling. We consider methods that can be applied for building cyber-physical systems and digital twins.
Tatiana Lazovskaya +2 more
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Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In the present paper we deal with a quasilinear problem involving a singular term and a parametric superlinear perturbation. We are interested in the existence, nonexistence and multiplicity of positive solutions as the parameter $\lambda>0$ varies.
Ricardo Alves
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Multiple positive solutions for singular anisotropic Dirichlet problems
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We consider a nonlinear Dirichlet problem driven by the variable exponent (anisotropic) $p$-Laplacian and a reaction that has the competing effects of a singular term and of a superlinear perturbation. There is no parameter in the equation (nonparametric
Zhenhai Liu, Nikolaos Papageorgiou
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Absolutely stable difference scheme for a general class of singular perturbation problems
Advances in Difference Equations, 2020 This paper presents an absolutely stable noniterative difference scheme for solving a general class of singular perturbation problems having left, right, internal, or twin boundary layers. The original two-point second-order singular perturbation problem
Essam R. El-Zahar +5 more
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A numerical approach for singular perturbation problems with an interior layer using an adaptive spline [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 An adaptive spline is used in this work to deal with singularly perturbed boundary value problems with layers in the interior region. To evaluate the layer behavior in the solution, a different technique on a uniform mesh is designed by replacing the ...
E. Srinivas, M. Lalu, K. Phaneendra
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Resonance for Singular Perturbation Problems [PDF]
SIAM Journal on Applied Mathematics, 1981 Consider the resonance for a second-order equation ey"-xpy’+ qy = 0. Another proof is given for the necessity of the Matkowsky condition and the connection with a regular eigenvalue problem is established. Also, if p, q are analytic, necessary and sufficient conditions are derived.
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