Symmetry breaking and semilinear elliptic equations
Journal of Computational and Applied Mathematics, 1989 Symmetry breaking bifurcations (SBB's) are studied which occur on the radially symmetric solution branches of the semilinear elliptic equation \(\Delta u+\lambda f(u)=0\) on the unit ball in the space \(R^ 3\). A general theory is developed which permits a straightforward calculation of the SBB's.
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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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Inverse problems for fractional semilinear elliptic equations [PDF]
Nonlinear Analysis, 2020 Ru-Yu Lai, Yi-Hsuan Lin
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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.
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Solutions of semilinear elliptic equations with one isolated singularity [PDF]
, 1999 Yomna Rébaı̈
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A Liouville theorem for a class semilinear elliptic equations on the Heisenberg group [PDF]
Advances in Mathematics, 2020 Xinan Ma, Q. Ou
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$1$D symmetry for solutions of semilinear and quasilinear elliptic equations [PDF]
, 2010 Alberto Farina, Enrico Valdinoci
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Nonradial Solutions of a Semilinear Elliptic Equation in Two Dimensions [PDF]
, 1993 Joseph A. Iaia, Henry A. Warchall
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Nonexistence of solutions to KPP-type equations of dimension greater than or equal to one
Electronic Journal of Differential Equations, 2006 In this article, we consider a semilinear elliptic equations of the form $Delta u+f(u)=0$, where $f$ is a concave function. We prove for arbitrary dimensions that there is no solution bounded in $(0,1)$.
Janos Englander, Peter L. Simon
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Harnack inequality for non-divergence structure semi-linear elliptic equations
Advances in Nonlinear Analysis, 2018 In this paper we establish a Harnack inequality for non-negative solutions of Lu=f(u){Lu=f(u)} where L is a non-divergence structure uniformly elliptic operator and f is a non-decreasing function that satisfies an appropriate growth conditions at ...
Mohammed Ahmed, Porru Giovanni
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