Existence and Multiplicity of Solutions for Fractional Elliptic Problems with Discontinuous Nonlinearities
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DOI: 10.1007/s00009-018-1188-7
Abstract: We consider the following fractional elliptic problem: $$\begin{aligned} (P)\left\{ \begin{array}{ll} (-\Delta )^s u = f(u) H(u-\mu )&{} \quad \text{ in } \ \Omega ,\\ u =0 &{}\quad \text{ on } \ \mathbb{{R}}^n {\setminus } \Omega… read more here.
Keywords: multiplicity solutions; existence multiplicity; solutions fractional; fractional elliptic ... See more keywords
Ultraconvergence of high order FEMs for elliptic problems with variable coefficients
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DOI: 10.1007/s00211-016-0838-6
Abstract: In this paper, we investigate local ultraconvergence properties of the high-order finite element method (FEM) for second order elliptic problems with variable coefficients. Under suitable regularity and mesh conditions, we show that at an interior… read more here.
Keywords: order; variable coefficients; problems variable; high order ... See more keywords
Expandable Parallel Finite Element Methods for Linear Elliptic Problems
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DOI: 10.1007/s10473-020-0218-2
Abstract: In this article, two kinds of expandable parallel finite element methods, based on two-grid discretizations, are given to solve the linear elliptic problems. Compared with the classical local and parallel finite element methods, there are… read more here.
Keywords: finite element; linear elliptic; parallel finite; expandable parallel ... See more keywords
Elliptic Problems with Boundary Conditions of Higher Orders in Hörmander Spaces
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DOI: 10.1007/s11253-018-1466-3
Abstract: In a class of inner-product Hörmander spaces, we study a general elliptic problem for which the maximum order of boundary conditions is not lower than the order of the elliptic equation. The role of the… read more here.
Keywords: higher orders; boundary conditions; conditions higher; problems boundary ... See more keywords
Positive Solutions for Elliptic Problems Involving Hardy–Sobolev–Maz’ya Terms
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DOI: 10.1007/s40840-018-0603-3
Abstract: In the present paper, we study the semilinear elliptic problem $$\displaystyle -\Delta u -\mu \frac{u}{|y|^{2}}=\frac{|u|^{2^{*}(s)-2}u}{|y|^{s}}+ f(x,u)$$-Δu-μu|y|2=|u|2∗(s)-2u|y|s+f(x,u) in bounded domain. Replacing the Ambrosetti–Rabinowitz condition by general superquadratic assumptions and the nonquadratic assumption, we establish the existence… read more here.
Keywords: problems involving; positive solutions; elliptic problems; hardy sobolev ... See more keywords
A painless automatic hp-adaptive strategy for elliptic problems
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DOI: 10.1016/j.finel.2020.103424
Abstract: In this work, we introduce a novel hp-adaptive strategy. The main goal is to minimize the complexity and implementational efforts hence increasing the robustness of the algorithm while keeping quasi-optimal results. We employ a multi-level… read more here.
Keywords: painless automatic; strategy elliptic; elliptic problems; strategy ... See more keywords
ESTIMATES AND RIGIDITY FOR STABLE SOLUTIONS TO SOME NONLINEAR ELLIPTIC PROBLEMS
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DOI: 10.1017/s0004972720000702
Abstract: where Ω is a bounded domain, p ∈ (1,+∞) and f is a C nonlinearity. This equation is the nonlinear version of the widely studied semilinear elliptic equation −∆u = f (u) in a bounded… read more here.
Keywords: rigidity stable; stable solutions; elliptic problems; estimates rigidity ... See more keywords
ON NONLOCAL NONLINEAR ELLIPTIC PROBLEMS WITH THE FRACTIONAL LAPLACIAN
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DOI: 10.1017/s0017089518000538
Abstract: Abstract In this paper, we study the existence of positive solutions to a semilinear nonlocal elliptic problem with the fractional α-Laplacian on Rn, 0 < α < n. We show that the problem has infinitely… read more here.
Keywords: problems fractional; fractional laplacian; nonlocal nonlinear; elliptic problems ... See more keywords
Nontrivial weak solutions for nonlocal nonhomogeneous elliptic problems
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DOI: 10.1080/00036811.2020.1778674
Abstract: This article concerns the following class of nonlocal nonhomogeneous elliptic problems: − ∫ Ω g ( x , u ) d x β div ( a ( x ) ∇ u ) = (… read more here.
Keywords: solutions nonlocal; weak solutions; nontrivial weak; nonlocal nonhomogeneous ... See more keywords
Singular elliptic problems with unbalanced growth and critical exponent
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DOI: 10.1088/1361-6544/ab81ed
Abstract: In this article, we study the existence and multiplicity of solutions of the following $(p,q)$-Laplace equation with singular nonlinearity: \begin{equation*} \left\{\begin{array}{rllll} -\Delta_{p}u-\ba\Delta_{q}u & = \la u^{-\de}+ u^{r-1}, \ u>0, \ \text{ in } \Om \\… read more here.
Keywords: unbalanced growth; critical exponent; growth critical; problems unbalanced ... See more keywords
Sublinear elliptic problems under radiality. Harmonic NA groups and Euclidean spaces
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DOI: 10.1515/forum-2019-0014
Abstract: Abstract Let ℒ {\mathcal{L}} be the Laplace operator on ℝ d {\mathbb{R}^{d}} , d ≥ 3 {d\geq 3} , or the Laplace–Beltrami operator on the harmonic NA group (in particular, on a rank one noncompact… read more here.
Keywords: harmonic groups; groups euclidean; sublinear elliptic; radiality harmonic ... See more keywords