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Sublinear Elliptic Equations With Singular Potentials
Advanced Nonlinear Studies, 2012 Abstract In this paper we prove existence and summability results for solutions of equations whose model is with a > 0 and f in some Marcinkiewicz space, thus ...
Lucio Boccardo, Luigi Orsina
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Estimates of singular numbers (s-numbers) for a class of degenerate elliptic operators [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2022 In this paper we study a class of degenerate elliptic equations with an arbitrary power degeneracy on the line. Based on the research carried out in the course of the work, the authors propose methods to overcome various difficulties associated with the
S.Zh. Igisinov +3 more
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Potentials for a three-dimensional elliptic equation with one singular coefficient and their application [PDF]
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2021 A potential theory for a three-dimensional elliptic equation with one singular coefficient is considered. Double- and simple-layer potentials with unknown density are introduced, which are expressed in terms of the fundamental solution of the mentioned ...
Tuhtasin G. Ergashev
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Potentials for the singular elliptic equations and their application
Results in Applied Mathematics, 2020 Potential theory has played a paramount role in both analysis and computation for boundary value problems for elliptic equations. In the middle of the last century, a potential theory was constructed for a two-dimensional elliptic equation with one ...
T.G. Ergashev
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SPECTRAL PROBLEMS FOR THREE-DIMENSIONAL ELLIPTIC EQUATIONS WITH SINGULAR COEFFICIENTS [PDF]
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2017 The eigenvalues and eigenfunctions of two boundary value problems for three-dimensional equations of elliptic types with singular coefficients with lower terms are found.
Karimov K. T.
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Advanced Nonlinear Studies, 2021 This paper establishes pointwise estimates up to boundary for the gradient of weak solutions to a class of very singular quasilinear elliptic equations with mixed ...
Do Tan Duc +2 more
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Existence of positive weak solutions for a class of singular elliptic equations
Electronic Journal of Qualitative Theory of Differential Equations, 2011 In this note, we are concerned with positive solutions for a class of singular elliptic equations. Under some conditions, we obtain weak solutions for the equations by elliptic regularization method and sub-super solution method.
Li Xia, Jingna Li, Zheng'an Yao
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On a Singular Elliptic Equation [PDF]
Proceedings of the American Mathematical Society, 1983 In this paper, we study the singular elliptic equation L u + K ( x
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A new existence result for some nonlocal problems involving Orlicz spaces and its applications
Boundary Value Problems, 2022 This paper studies some quasilinear elliptic nonlocal equations involving Orlicz–Sobolev spaces. On the one hand, a new sub-supersolution theorem is proved via the pseudomonotone operator theory; on the other hand, using the obtained theorem, we present ...
Xiaohui Qiu, Baoqiang Yan
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Elliptic equations with singularity on the boundary
Differential and Integral Equations, 1999 Positive solutions of the nonlinear elliptic problem \(-\Delta u (x)=K(x)(1-| x| )^{-\alpha }u^\beta (x)\) on the unit ball \(B\), with zero boundary values, are studied. \(K\) is a nonnegative continuous function on \(\overline B\), positive on \(\partial B\).
Hashimoto, Satoshi, Ôtani, Mitsuharu
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