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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Dimension of the set of positive solutions to nonlinear equations and applications
Electronic Journal of Differential Equations, 2016 We study the covering dimension of the set of (positive) solutions to various classes of nonlinear equations involving condensing and A-proper maps. It is based on the nontriviality of the fixed point index of a certain condensing map or on oddness ...
Petronije S. Milojevic
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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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Generalized Harnack inequality for semilinear elliptic equations
Journal de Mathématiques Pures et Appliquées, 2016 This paper is concerned with semilinear equations in divergence form \[ \diver(A(x)Du) = f(u) \] where $f :\R \to [0,\infty)$ is nondecreasing. We prove a sharp Harnack type inequality for nonnegative solutions which is closely connected to the classical Keller-Osserman condition for the existence of entire solutions.
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Concentration and dynamic system of solutions for semilinear elliptic equations
Electronic Journal of Differential Equations, 2003 In this article, we use the concentration of solutions of the semilinear elliptic equations in axially symmetric bounded domains to prove that the equation has three positive solutions. One solution is y-symmetric and the other are non-axially symmetric.
Tsung-fang Wu
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Solving Fredholm Integral Equations Using Deep Learning. [PDF]
Int J Appl Comput Math, 2022 Guan Y, Fang T, Zhang D, Jin C.
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On oscillating radial solutions for non-autonomous semilinear elliptic equations
AIMS MathematicsWe consider semilinear elliptic equations of the form $ \Delta u + f(|x|, u) = 0 $ on $ {\mathbb{R}}^{N} $ with $ f(|x|, u) = q(|x|)g(u) $. These type of equations arise in various problems in applied mathematics, and particularly in the study of ...
H. Al Jebawy, H. Ibrahim, Z. Salloum
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Nodal solutions to semilinear elliptic equations in a ball
Differential and Integral Equations, 2002 The paper is concerned with the existence and multiplicity of radial solutions to the equation \(\Delta u+q(|x|)g(u)=0\) on the unit ball \(\Omega\subset\mathbb{R}^N\) with homogeneous Dirichlet boundary conditions. It is assumed that \(q:[0,1] \to (0,\infty)\) is continuous and \(q(r)\geq q_0>0\) for \(r\in[r_1,r_2]\subset(0,1]\). The nonlinearity \(g:
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A singular perturbation result for a class of periodic-parabolic BVPs
Open MathematicsIn this article, we obtain a very sharp version of some singular perturbation results going back to Dancer and Hess [Behaviour of a semilinear periodic-parabolic problem when a parameter is small, Lecture Notes in Mathematics, Vol. 1450, Springer-Verlag,
Cano-Casanova Santiago +2 more
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