Solutions to nonlinear elliptic equations with a nonlocal boundary condition
Electronic Journal of Differential Equations, 2002 We study an elliptic equation and its evolution problem on a bounded domain with nonlocal boundary conditions. Eigenvalue problems, existence, and dynamic behavior of solutions for linear and semilinear equations are investigated.
Yuandi Wang
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Computation of radial solutions of semilinear equations
Electronic Journal of Qualitative Theory of Differential Equations, 2007 We express radial solutions of semilinear elliptic equations on $R^n$ as convergent power series in $r$, and then use Pade approximants to compute both ground state solutions, and solutions to Dirichlet problem.
Philip Korman
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The Topological State Derivative: An Optimal Control Perspective on Topology Optimisation. [PDF]
J Geom Anal, 2023 Baumann P, Mazari-Fouquer I, Sturm K.
europepmc +1 more source
A Liouville theorem for a class semilinear elliptic equations on the Heisenberg group [PDF]
Advances in Mathematics, 2020 Xinan Ma, Q. Ou
semanticscholar +1 more source
Some maximum principles in semilinear elliptic equations [PDF]
Proceedings of the American Mathematical Society, 1986 We develop maximum principles for functions defined on the solutions to a class of semilinear, second order, uniformly elliptic partial differential equations. These principles are related to recent theorems of Protter and Protter and Weinberger and to a technique initiated by Payne for the determination of gradient bounds on the solution of the ...
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On the solution stability of parabolic optimal control problems. [PDF]
Comput Optim Appl, 2023 Corella AD, Jork N, Veliov VM.
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A priori bounds for positive solutions of a semilinear elliptic equation [PDF]
, 1985 Chris Cosner, Klaus Schmitt
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Multiplicity of Nontrivial Solutions of Semilinear Elliptic Equations
Journal of Mathematical Analysis and Applications, 2000 It is considered the following problem: \(-\Delta u = f(x,u)\) in \(\Omega\), \(u=0\) on \(\partial\Omega\), where \(f\) is a subcritical Carathéodory function. It is proved the existence of at least two nontrivial solutions. This paper unifies and generalizes some results from \textit{A. Castro} and \textit{A. C. Lazer} [Ann. Mat. Pura Appl., IV. Ser.
Chun-Lei Tang +2 more
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Oscillation criteria for semilinear elliptic equations with a damping term in R^n
Electronic Journal of Differential Equations, 2010 We use a method based on Picone-type identities to find oscillation conditions for the equation $$ sum_{i j =1}^n frac{partial}{partial x_i} Big( a_{ij}(x) frac{partial}{partial x_j} Big)u + f(x,u, abla u) + c(x) u =0,, $$ with Dirichlet boundary ...
Tadie
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Comparison results for semilinear elliptic equations via Picone-type identities
Electronic Journal of Differential Equations, 2009 By means of a Picone's type identity, we prove uniqueness and oscillation of solutions to an elliptic semilinear equation with Dirichlet boundary conditions.
Tadie
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