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Essential spectra of elliptic partial differential equations [PDF]
Bulletin of the American Mathematical Society, 1967 Let A be a closed, densely defined operator in a Banach space X. There are several definitions of the "essential" spectrum of A (cf. [ l ] , [2]). According to Wolf [3], [4] it is the complement in the complex plane of the $-set of A. The $-set $A of A is the set of points X for which (a) a(A — X), the dimension of the null space of A — X, is finite (b)
Martin Schechter
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Lectures on Elliptic Partial Differential Equations
, 2018 The volume develops several basic classical topics of the qualitative theory of elliptic partial differential equations and calculus of variations, including recent contributions to partial regularity for systems and the theory of viscosity solutions. The content is divided into the following five chapters: I.
Luigi Ambrosio +2 more
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A Solution Method for Differential Equations Based on Taylor PINN
IEEE Access, 2023 Based on deep neural network, elliptic partial differential equations in complex regions are solved. Accurate and effective strategies and numerical methods for elliptic partial differential equations are proposed by implementing deep feedforward ...
Yajuan Zhang +3 more
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On elliptic partial differential equations in bioimpedance [PDF]
Journal of Elliptic and Parabolic Equations, 2020 AbstractThis paper deals with mathematical models in electrical bioimpedance fields that are described by means of elliptic partial differential equations (PDEs). To find solutions that have practical significance and value, it is necessary to gain a deep understanding of the underlying physical phenomena with the parameter details of PDE models as ...
Jin Keun Seo +2 more
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An elliptic partial differential equation and its application [PDF]
Applied Mathematics Letters, 2020 This paper deals with the following elliptic equation \begin{equation*} -2 ^{2} z+\left\| \nabla z\right\| ^{2}+4 z=4\left\| x\right\| ^{2}\text{ for }x\in \mathbb{R}^{N}\text{, (}% N\geq 1\text{),} \end{equation*}% where $ >0,$ $ >0$ are some real parameters. The solution method is based on the sub- and super-solutions approach. The case $N&
Dragos-Patru Covei, Traian A. Pirvu
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International Journal of Mathematics and Mathematical Sciences, 2020 In this article, we utilize the G′/G2-expansion method and the Jacobi elliptic equation method to analytically solve the (2 + 1)-dimensional integro-differential Jaulent–Miodek equation for exact solutions.
Supaporn Kaewta +2 more
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Differential-Difference Elliptic Equations with Nonlocal Potentials in Half-Spaces
Mathematics, 2023 We investigate the half-space Dirichlet problem with summable boundary-value functions for an elliptic equation with an arbitrary amount of potentials undergoing translations in arbitrary directions.
Andrey B. Muravnik
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Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations
International Journal of Mathematics and Mathematical Sciences, 1989 The decomposition method is applied to examples of hyperbolic, parabolic, and elliptic partial differential equations without use of linearizatlon techniques.
G. Adomian
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The Extended Trial Equation Method for Some Time Fractional Differential Equations
Discrete Dynamics in Nature and Society, 2013 Nonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. Based on the fractional derivative in the sense of modified Riemann-Liouville derivative and traveling wave transformation, the ...
Yusuf Pandir +2 more
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Journal of Applied Mathematics, 2013 We use the improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method to construct some of the generalized Jacobi elliptic solutions for some nonlinear partial differential equations in mathematical ...
Khaled A. Gepreel
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