Least energy nodal solutions for elliptic equations with indefinite nonlinearity [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2014 We prove the existence of a nodal solution with two nodal domains for the Dirichlet problem with indefinite nonlinearity \begin{equation*} -\Delta_p u = \lambda |u|^{p-2} u + f(x) |u|^{\gamma-2} u \end{equation*} in a bounded domain $\Omega \subset ...
Vladimir Bobkov
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Nodal Solutions of the p-Laplacian with Sign-Changing Weight [PDF]
Abstract and Applied Analysis, 2013 We are concerned with determining values of , for which there exist nodal solutions of the boundary value problem , where is a sign-changing function, with . The proof of our main results is based upon global bifurcation techniques.
Ruyun Ma, Xilan Liu, Jia Xu
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Multiple nodal solutions of nonlinear Choquard equations [PDF]
Electronic Journal of Differential Equations, 2017 In this article, we consider the existence of multiple nodal solutions of the nonlinear Choquard equation $$\displaylines{ -\Delta u+u=(|x|^{-1}\ast|u|^p)|u|^{p-2}u \quad \text{in }\mathbb{R}^3,\cr u\in H^1(\mathbb{R}^3), }$$ where $p\in (5/2,5 ...
Zhihua Huang, Jianfu Yang, Weilin Yu
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Multiplicity of positive and nodal solutions for scalar field equations
Journal of Differential Equations, 2014 The authors are concerned with the scalar field equation \(-\Delta u+a(x) u=|u|^{p-2}u\) in \({\mathbb R}^N\), where \(N\geq 2 ...
Giovanna Cerami +2 more
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The nodal set of solutions to anomalous equations [PDF]
Bruno Pini Mathematical Analysis Seminar, 2019 This note focuses on the geometric-theoretic analysis of the nodal set of solutions to specific degenerate or singular equations. As they belong to the Muckenhoupt class A_2, these operators appear in the seminal works of Fabes, Kenig, Jerison and ...
Giorgio Tortone
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Oddness of least energy nodal solutions on radial domains [PDF]
Electronic Journal of Differential Equations, 2010 In this article, we consider the Lane-Emden problem $$displaylines{ Delta u(x) + |{u(x)}mathclose|^{p-2}u(x)=0, quad hbox{for } xinOmega,cr u(x)=0, quad hbox{for } xinpartialOmega, }$$ where $2 < p < 2^{*}$ and $Omega$ is a ball or an annulus
Christopher Grumiau +1 more
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Nodal Solutions for Supercritical Laplace Equations [PDF]
Communications in Mathematical Physics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
F. Dalbono, M. Franca
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Symmetry of Nodal Solutions for Singularly Perturbed Elliptic Problems on a Ball [PDF]
, 2004 In [40], it was shown that the following singularly perturbed Dirichlet problem \ep^2 \Delta u - u+ |u|^{p-1} u=0, \ \mbox{in} \ \Om,\] \[ u=0 \ \mbox{on} \ \partial \Om has a nodal solution u_\ep which has the least energy among all nodal solutions.
Winter, M +5 more
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Analysis of the asymmetrically expressed Ablim1 locus reveals existence of a lateral plate Nodal-independent left sided signal and an early, left-right independent role for nodal flow. [PDF]
, 2010 BACKGROUND: Vertebrates show clear asymmetry in left-right (L-R) patterning of their organs and associated vasculature. During mammalian development a cilia driven leftwards flow of liquid leads to the left-sided expression of Nodal, which in turn ...
Norris, Dominic P. +23 more
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A novel Nodal enhancer dependent on pluripotency factors and Smad2/3 signaling conditions a regulatory switch during epiblast maturation [PDF]
, 2014 During early development, modulations in the expression of Nodal, a TGFβ family member, determine the specification of embryonic and extra-embryonic cell identities.
Jérôme Collignon (34631) +39 more
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