Results 31 to 40 of about 75,181 (273)
Semilinear elliptic equations and supercritical growth
Journal of Differential Equations, 1987 \textit{H. Brezis} and \textit{L. Nirenberg} have proved the existence of positive solutions of the problem \(\Delta \tilde u+\lambda \tilde u+\tilde u^ p=0\) in \(\Omega\) and \(\tilde u=0\) on \(\partial \Omega\) for \(p\leq p_ c=(n+2)/(n-2)\), when the embedding of \(H^ 1_ 0(\Omega)\) in \(L^{p+1}(\Omega)\) is continuous [Commun. Pure Appl. Math. 36,
Budd, C, Norbury, J
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Topological Derivatives for Semilinear Elliptic Equations [PDF]
International Journal of Applied Mathematics and Computer Science, 2009 Topological Derivatives for Semilinear Elliptic EquationsThe form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in theL∞norm are obtained.
Iguernane, Mohamed +4 more
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A new proof of the boundedness results for stable solutions to semilinear elliptic equations [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2019 We consider the class of stable solutions to semilinear equations $-\Delta u=f(u)$ in a bounded smooth domain of $\mathbb{R}^n$. Since 2010 an interior a priori $L^\infty$ bound for stable solutions is known to hold in dimensions $n \leq 4$ for all $C^1$
X. Cabré
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On the existence of multiple positive entire solutions for a class of quasilinear elliptic equations
International Journal of Mathematics and Mathematical Sciences, 2006 Our goal is to establish the theorems of existence and multiple of positive entire solutions for a class quasilinear elliptic equations in ℝN with the Schauder-Tychonoff fixed point theorem as the principal tool.
Yang Zuodong
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Boundedness of Stable Solutions to Semilinear Elliptic Equations: A Survey [PDF]
, 2017 This article is a survey on boundedness results for stable solutions to semilinear elliptic problems.For these solutions, we present the currently known L∞${L^{\infty}}$ estimates that hold for all nonlinearities.Such estimates are known to hold up to ...
X. Cabré
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On the exact multiplicity of stable ground states of non-Lipschitz semilinear elliptic equations for some classes of starshaped sets [PDF]
Advances in Nonlinear Analysis, 2018 We prove the exact multiplicity of flat and compact support stable solutions of an autonomous non-Lipschitz semilinear elliptic equation of eigenvalue type according to the dimension N and the two exponents, 0 < α < β < 1, of the involved nonlinearites ...
J. Díaz +2 more
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Journal of Function Spaces, 2020 In this paper, we study multiplicity of positive solutions for a class of semilinear elliptic equations with the nonlinearity containing singularity and Hardy-Sobolev exponents.
Yong-Yi Lan, Xian Hu, Bi-Yun Tang
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Barekeng, 2023 Let be a bounded open subset of , , be a function in Stummel classes , where , and be a semilinear monotone elliptic equation, where is symmetric matrix, elliptic, bounded, and is non decreasing and Lipschitz. By proving a weighted estimation for
Nicky Kurnia Tumalun
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Analysis of control problems of nonmontone semilinear elliptic equations [PDF]
, 2019 In this paper we study optimal control problems governed by a semilinear elliptic equation. The equation is nonmonotone due to the presence of a convection term, despite the monotonocity of the nonlinear term.
E. Casas, M. Mateos, A. Rösch
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Asymptotic solutions of semilinear elliptic equations
Journal of Mathematical Analysis and Applications, 1984 Semilinear elliptic equations of the form \(Lu\equiv \Delta u-p(| x|)u+uf(x,u)=0\) are considered in exterior domains in \({\mathbb{R}}^ n\) for \(n\geq 2\). Both necessary and sufficient conditions are established for such equations to have positive solutions with prescribed asymptotic behavior as \(| x| \to \infty\).
Charles A. Swanson, Kurt Kreith
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