Results 31 to 40 of about 15,562 (203)
Locating the peaks of semilinear elliptic systems
, 2005 We consider a system of weakly coupled singularly perturbed semilinear elliptic equations. First, we obtain a Lipschitz regularity result for the associated ground energy function $\Sigma$ as well as representation formulas for the left and the right ...
Pomponio, Alessio, Squassina, Marco
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Symmetry and concentration behavior of ground state in axially symmetric domains
Abstract and Applied Analysis, 2004 We let Ω(r) be the axially symmetric bounded domains which satisfy some suitable conditions, then the ground-state solutions of the semilinear elliptic equation in Ω(r) are nonaxially symmetric and concentrative on one side.
Tsung-Fang Wu
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On Semilinear Elliptic Equation with Measurable Nonlinearity [PDF]
, 2015 We consider a semilinear elliptic equation in a bounded domain with zero boundary conditions. The nonlinearity is discontinuous and monotone, but it is not a Carath\'eodory's function.
Zubelevich, Oleg
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Zero Sets of Solutions to Semilinear Elliptic Systems of First Order
, 1998 Consider a nontrivial solution to a semilinear elliptic system of first order with smooth coefficients defined over an $n$-dimensional manifold. Assume the operator has the strong unique continuation property. We show that the zero set of the solution is
Baer, Christian
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Multiple front and pulse solutions in spatially periodic systems
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract In this paper, we develop a comprehensive mathematical toolbox for the construction and spectral stability analysis of stationary multiple front and pulse solutions to general semilinear evolution problems on the real line with spatially periodic coefficients.
Lukas Bengel, Björn de Rijk
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On a semilinear elliptic equation with inverse square potential [PDF]
, 2008 On a semilinear elliptic equation with inverse square ...
Brezis, Haïm +2 more
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Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract In this paper, we investigate the following D1,p$D^{1,p}$‐critical quasi‐linear Hénon equation involving p$p$‐Laplacian −Δpu=|x|αupα∗−1,x∈RN,$$\begin{equation*} -\Delta _p u=|x|^{\alpha }u^{p_\alpha ^*-1}, \qquad x\in \mathbb {R}^N, \end{equation*}$$where N⩾2$N\geqslant 2$, 1
Wei Dai +3 more
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Multiple Nontrivial Solutions of Semilinear Elliptic Equations [PDF]
Proceedings of the American Mathematical Society, 1988 We give a condition for a semilinear elliptic equation to have two nontrivial solutions. Our condition does not demand any differentiability of the nonlinear term.
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Large‐Amplitude Periodic Solutions to the Steady Euler Equations With Piecewise Constant Vorticity
Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.ABSTRACT We consider steady solutions to the incompressible Euler equations in a two‐dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation theory, we rigorously construct curves of solutions that terminate either with stagnation on the interface ...
Alex Doak +3 more
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Semilinear elliptic equations on rough domains
Journal of Differential Equations, 2023 39 ...
Wolfgang Arendt, Daniel Daners
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