Multigrid method for coupled semilinear elliptic equation
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DOI: 10.1002/mma.5543
Abstract: This paper introduces a kind of multigrid finite element method for the coupled semilinear elliptic equations. Instead of the common way of directly solving the coupled semilinear elliptic problems on some fine spaces, the presented… read more here.
Keywords: method coupled; semilinear elliptic; coupled semilinear; elliptic equation ... See more keywords
A novel domain decomposition method for coupled semilinear elliptic equation
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DOI: 10.1002/mma.7415
Abstract: This study presents a new framework to solve the coupled semilinear elliptic equation by the domain decomposition algorithm. Unlike the traditional domain decomposition algorithm, the coupled semilinear elliptic equation doesn't need to be solved directly.… read more here.
Keywords: semilinear elliptic; decomposition; elliptic equation; coupled semilinear ... See more keywords
Characterization of the Critical Value for a Quasilinear Elliptic Equation with Arbitrary Growth with Respect to the Gradient
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DOI: 10.1007/s00009-019-1413-z
Abstract: The aim of this work is to study a quasilinear elliptic equation where we are particularly interested in the characterization of the critical value, which appears as the Lagrange multiplier in the functional minimization associated… read more here.
Keywords: elliptic equation; characterization critical; quasilinear elliptic; critical value ... See more keywords
Gradient estimates of a nonlinear elliptic equation for the V-Laplacian
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DOI: 10.1007/s00013-019-01419-1
Abstract: This paper studies gradient estimates for positive solutions of the nonlinear elliptic equation $$\begin{aligned} \Delta _V(u^p)+\lambda u=0,\quad p\ge 1, \end{aligned}$$on a Riemannian manifold (M, g) with k-Bakry–Emery Ricci curvature bounded from below. We consider both the… read more here.
Keywords: gradient estimates; estimates nonlinear; nonlinear elliptic; elliptic equation ... See more keywords
Large solutions of a semilinear elliptic equation with singular weights and nonhomogeneous term
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DOI: 10.1007/s00013-019-01432-4
Abstract: In this paper, we shall investigate a semilinear elliptic boundary blow-up problem $$\Delta u=a(x)|u|^{p-1}u+h(x)$$ Δ u = a ( x ) | u | p - 1 u + h ( x ) in $$\Omega… read more here.
Keywords: solutions semilinear; nonhomogeneous term; semilinear elliptic; elliptic equation ... See more keywords
Bifurcation results for a fractional elliptic equation with critical exponent in $$\mathbb {R}^n$$Rn
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DOI: 10.1007/s00229-016-0878-3
Abstract: In this paper we study some nonlinear elliptic equations in $${\mathbb R}^n$$Rn obtained as a perturbation of the problem with the fractional critical Sobolev exponent, that is $$\begin{aligned} (-\Delta )^s u = \varepsilon \,h\,u_+^q + u_+^p… read more here.
Keywords: bifurcation results; fractional elliptic; results fractional; elliptic equation ... See more keywords
Classification of Stable Solutions to a Fractional Singular Elliptic Equation with Weight
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DOI: 10.1007/s10440-020-00347-5
Abstract: Let $p>0$ and $(-\Delta )^{s}$ is the fractional Laplacian with $0< s2s$ and $h$ is a nonnegative, continuous function satisfying $h(x)\geq C|x|^{a}$ , $a\geq 0$ , when $|x|$ large. We prove the nonexistence of positive… read more here.
Keywords: solutions fractional; fractional singular; elliptic equation; equation weight ... See more keywords
Periodic solutions of a semilinear elliptic equation with a fractional Laplacian
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DOI: 10.1007/s11784-016-0357-1
Abstract: We consider periodic solutions of the following problem associated with the fractional Laplacian $$(-\partial _{xx})^s u(x) + F'(u(x))=0,\quad u(x)=u(x+T),\quad \text{ in } \, \mathbb {R}, $$(-∂xx)su(x)+F′(u(x))=0,u(x)=u(x+T),inR,where $$(-\partial _{xx})^s$$(-∂xx)s denotes the usual fractional Laplace operator with… read more here.
Keywords: equation fractional; solutions semilinear; periodic solutions; fractional laplacian ... See more keywords
Existence of weak and renormalized solutions of degenerated elliptic equation
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DOI: 10.1007/s13370-019-00682-3
Abstract: We consider the degenerate nonlinear elliptic equation (E) : $${\mathcal {A}}(u)= g-{\text {div}}(f)$$A(u)=g-div(f), where $${\mathcal {A}}(u)=-{\text {div}}(a(x,u,\nabla u))$$A(u)=-div(a(x,u,∇u)) is a Leray-Lions operator defined on $$W_0^{1,p(\cdot )}(\Omega )$$W01,p(·)(Ω) allowed to be non linear degenerated. The main… read more here.
Keywords: elliptic equation; weak renormalized; existence weak; cdot ... See more keywords
Liouville theorems to semi-linear degenerate elliptic equation of generalized Baouendi-Grushin vector fields
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DOI: 10.1016/j.jde.2021.02.016
Abstract: Abstract In this paper we investigate a semi-linear degenerate elliptic equation Δ L u + h ( ξ ) u p + g ( ξ ) u q = 0 related to the generalized Baouendi-Grushin… read more here.
Keywords: generalized baouendi; baouendi grushin; degenerate elliptic; elliptic equation ... See more keywords
Positive clusters for smooth perturbations of a critical elliptic equation in dimensions four and five
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DOI: 10.1016/j.jfa.2018.02.002
Abstract: We construct clustering positive solutions for a perturbed critical elliptic equation on a closed manifold of dimension $n=4,5$. Such a construction is already available in the literature in dimensions $n\ge 6$ (see for instance [8,12,27,29,33])… read more here.
Keywords: positive clusters; elliptic equation; clusters smooth; smooth perturbations ... See more keywords