Integer Solutions of Matrix Linear Unilateral and Bilateral Equations over Quadratic Rings
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DOI: 10.1007/s10958-017-3337-0
Abstract: For matrix linear equations AX + BY = C and AX + YB = C over quadratic rings ℤk$$ \mathbb{Z}\left[\sqrt{k}\right] $$, we establish necessary and sufficient conditions for the existence of integer solutions, i.e., solutions… read more here.
Keywords: integer solutions; equations quadratic; matrix linear; solutions matrix ... See more keywords
Sobolev multipliers, maximal functions and parabolic equations with a quadratic nonlinearity
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DOI: 10.1016/j.jfa.2017.11.009
Abstract: Abstract We develop a general framework to describe global mild solutions to a Cauchy problem with small initial values concerning a general class of semilinear parabolic equations with a quadratic nonlinearity. This class includes the… read more here.
Keywords: equations quadratic; multipliers maximal; quadratic nonlinearity; parabolic equations ... See more keywords
Singular elliptic equations with quadratic gradient term
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DOI: 10.1016/j.jmaa.2021.125245
Abstract: Abstract We establish the existence of a non-trivial weak solution to the following singular quasilinear equation with Hardy potential and singular quadratic gradient term: { − Δ u − μ u | x | 2… read more here.
Keywords: quadratic gradient; gradient term; elliptic equations; singular elliptic ... See more keywords
Inverse problems for difference equations with quadratic eigenparameter dependent boundary conditions
Sign Up to like & getrecommendations! Published in 2017 at "Quaestiones Mathematicae"
DOI: 10.2989/16073606.2017.1334156
Abstract: Abstract This paper inductively investigates an inverse problem for difference boundary value problems with boundary conditions that depend quadratically on the eigenparameter. In particular, given the eigenvalues and the weights, we provide an algorithm to… read more here.
Keywords: difference equations; difference; equations quadratic; boundary conditions ... See more keywords