Results 21 to 30 of about 394,604 (313)
On the Cauchy problem for semilinear elliptic equations [PDF]
Journal of Inverse and Ill-posed Problems, 2015 Abstract We study the Cauchy problem for nonlinear (semilinear) elliptic partial differential equations in Hilbert spaces. The problem is severely ill-posed in the sense of Hadamard. Under a weak a priori assumption on the exact solution, we propose a new regularization method for stabilising the ill-posed problem.
Daniel Lesnic +3 more
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Bubble towers for supercritical semilinear elliptic equations [PDF]
Journal of Functional Analysis, 2005 We construct positive solutions of the semilinear elliptic problem $ u+ u + u^p = 0$ with Dirichet boundary conditions, in a bounded smooth domain $ \subset \R^N$ $(N\geq 4)$, when the exponent $p$ is supercritical and close enough to $\frac{N+2}{N-2}$ and the parameter $ \in\R$ is small enough.
Ruihua Jing +3 more
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Semilinear elliptic equations on manifolds with nonnegative Ricci curvature [PDF]
Journal of the European Mathematical Society (Print), 2022 In this paper we prove classification results for solutions to subcritical and critical semilinear elliptic equations with a nonnegative potential on noncompact manifolds with nonnegative Ricci curvature.
G. Catino, D. Monticelli
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Semilinear elliptic equations involving mixed local and nonlocal operators [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2020 In this paper, we consider an elliptic operator obtained as the superposition of a classical second-order differential operator and a nonlocal operator of fractional type. Though the methods that we develop are quite general, for concreteness we focus on
Stefano Biagi +3 more
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Monotonicity-based inversion of fractional semilinear elliptic equations with power type nonlinearities [PDF]
Calculus of Variations and Partial Differential Equations, 2020 We investigate the monotonicity method for fractional semilinear elliptic equations with power type nonlinearities. We prove that if-and-only-if monotonicity relations between coefficients and derivatives of the Dirichlet-to-Neumann map hold.
Yi-Hsuan Lin
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On Semilinear Elliptic Equation with Measurable Nonlinearity [PDF]
arXiv, 2013 this paper has been withdrawn by the author due to the results on the whole are not ...
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Nondegeneracy of the bubble solutions for critical equations involving the polyharmonic operator
Boundary Value Problems, 2023 We reprove a result by Bartsch, Weth, and Willem (Calc. Var. Partial Differ. Equ. 18(3):253–268, 2003) concerning the nondegeneracy of bubble solutions for a critical semilinear elliptic equation involving the polyharmonic operator.
Dandan Yang +3 more
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Stable solutions to semilinear elliptic equations are smooth up to dimension $9$ [PDF]
Acta Mathematica, 2019 In this paper we prove the following long-standing conjecture: stable solutions to semilinear elliptic equations are bounded (and thus smooth) in dimension $n \leq 9$. This result, that was only known to be true for $n\leq4$, is optimal: $\log(1/|x|^2)$
X. Cabré +3 more
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AIMS Mathematics, 2022 This paper aims to construct a two-grid mixed finite element scheme for distributed optimal control governed by semilinear elliptic equations. The state and co-state are approximated by the $ P_0^2 $-$ P_1 $ pair and the control variable is approximated ...
Changling Xu, Hongbo Chen
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Semilinear problems with bounded nonlinear term
Boundary Value Problems, 2005 We solve boundary value problems for elliptic semilinear equations in which no asymptotic behavior is prescribed for the nonlinear term.
Martin Schechter
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