Continuous Differentiability of the Value Function of Semilinear Parabolic Infinite Time Horizon Optimal Control Problems on L 2 ( Ω ) Under Control Constraints. [PDF]
Appl Math Optim, 2022 Kunisch K, Priyasad B.
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Semilinear elliptic equations with measure data and quasi-regular Dirichlet forms [PDF]
, 2016 Tomasz Klimsiak, Andrzej Rozkosz
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Uniqueness of Positive Solutions of Semilinear Elliptic Equations
Journal of Differential Equations, 1995 The uniqueness of positive solutions of the problem \[ \Delta u+ f(u)= 0, \quad u>0,\;x\in B_ R, \qquad u|_{\partial B_ R}=0, \] where \(f(u)\geq 0\), \(B_ R\) is a ball with radius \(R\) in \(\mathbb{R}^ n\), \(n>2\), is studied. The following nonlinearities \(f\) are considered: \(f(u)= u^ p+ u^ q\) and the more general case \(f(u)= \sum_{i=1}^ k a_ ...
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Inverse eigenvalue problems for semilinear elliptic equations
Electronic Journal of Differential Equations, 2009 We consider the inverse nonlinear eigenvalue problem for the equation $$displaylines{ -Delta u + f(u) = lambda u, quad u > 0 quad hbox{in } Omega,cr u = 0 quad hbox{on } partialOmega, } where $f(u)$ is an unknown nonlinear term, $Omega subset ...
Tetsutaro Shibata
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Constrained Nonlinear and Mixed Effects Integral Differential Equation Models for Dynamic Cell Polarity Signaling. [PDF]
Front Plant Sci, 2022 Xiao Z +5 more
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Multiple solutions of nonlinear fractional elliptic equations via Morse theory
Electronic Journal of Differential Equations, 2017 This article concerns the existence and multiplicity of weak solutions of the nonlinear fractional elliptic problem. We extend some well known results of semilinear Laplacian equations to the nonlocal fractional setting. Using the variational methods
Wei Qi, Lin Zhao, Xingjie Yan
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A free boundary problem for semilinear elliptic equations
, 1986 The regularity of the free boundary for the following problem was investigated: \[ \Delta u=a(x,u)\gamma u^{\gamma -1}\text{ on } \Omega \cap \{u>0\},\quad 00\}\) where a tangent plane in measure exists, which is denoted by \(\partial_{red}\{u>0\};\) 3) A notion of 'flat' free boundary point was introduced; 4) The \(C^{1,\alpha}\) surface regularity of
Alt, H.W., Phillips, D.
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Elastic anisotropy in the reduced Landau-de Gennes model. [PDF]
Proc Math Phys Eng Sci, 2022 Han Y, Harris J, Majumdar A, Zhang L.
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An inverse boundary-value problem for semilinear elliptic equations
Electronic Journal of Differential Equations, 2010 We show that in dimension two or greater, a certain equivalence class of the scalar coefficient $a(x,u)$ of the semilinear elliptic equation $Delta u,+a(x,u)=0$ is uniquely determined by the Dirichlet to Neumann map of the equation on a bounded ...
Ziqi Sun
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Multiplicity results for nonlinear elliptic equations
Electronic Journal of Differential Equations, 2006 Let $Omega$ be a bounded domain in $mathbb{R}^{N}$, $Ngeq 3$, and $p=frac{2N}{N-2}$ the limiting Sobolev exponent. We show that for $fin H^1_0(Omega)^ast$, satisfying suitable conditions, the nonlinear elliptic problem $$displaylines{ -Delta u =|u |^{ p ...
Samira Benmouloud +2 more
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