A Counterexample for Singular Equations with Indefinite Weight
Advanced Nonlinear Studies, 2017 We construct a second-order equation x¨=h(t)/xp{\ddot{x}=h(t)/x^{p}}, with p>1{p>1} and the sign-changing, periodic weight function h having negative mean, which does not have periodic solutions.
Ureña Antonio J.
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Multiple Solutions for a Class of N-Laplacian Equations with Critical Growth and Indefinite Weight [PDF]
Abstract and Applied Analysis, 2014 Using the suitable Trudinger-Moser inequality and the Mountain Pass Theorem, we prove the existence of multiple solutions for a class of N-Laplacian equations with critical growth and indefinite weight -div∇uN-2∇u+VxuN-2u=λuN-2u/xβ+fx,u/xβ+ɛhx, x∈ℝN, u≠0,
Guoqing Zhang, Ziyan Yao
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Spectrum of one dimensional p-Laplacian operator with indefinite weight [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2002 This paper is concerned with the nonlinear boundary eigenvalue problem $$-(|u'|^{p-2}u')'=\lambda m|u|^{p-2}u\qquad u \in I=]a,b[,\quad u(a)=u(b)=0,$$ where $p>1$, $\lambda$ is a real parameter, $m$ is an indefinite weight, and $a$, $b$ are real numbers.
Mohammed Moussa, A. Anane, Omar Chakrone
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Eigenvalues and bifurcation for Neumann problems with indefinite weights
Electronic Journal of Differential Equations, 2021 We consider eigenvalue problems and bifurcation of positive solutions for elliptic equations with indefinite weights and with Neumann boundary conditions.
Marta Calanchi, Bernhard Ruf
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Existence Results for Quasilinear Elliptic Equations with Indefinite Weight [PDF]
Abstract and Applied Analysis, 2012 We provide the existence of a solution for quasilinear elliptic equation −div(𝑎∞(𝑥)|∇𝑢|𝑝−2∇𝑢+̃𝑎(𝑥,|∇𝑢|)∇𝑢)=𝜆𝑚(𝑥)|𝑢|𝑝−2𝑢+𝑓(𝑥,𝑢)+ℎ(𝑥) in Ω under the Neumann boundary condition.
Mieko Tanaka
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On the antimaximum principle for the p-Laplacian with indefinite weight
Nonlinear Analysis: Theory, Methods & Applications, 2001 A study of the antimaximum principle (AMP) for a class of equations involving the p-Laplacian operator with indefinite weights was presented. The AMP was extended to the case of a linear operator with weight and to the case of a nonlinear operator ...
Gossez, Jean-Pierre +6 more
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A spectral problem with an indefinite weight for an elliptic system [PDF]
Electronic Journal of Differential Equations, 1997 We establish the completeness and the summability in the sense of Abel-Lidskij of the root vectors of a non-selfadjoint elliptic problem with an indefinite weight matrix and the angular distribution of its eigenvalues.
Mamadou Sango
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Bifurcation in nonlinearizable eigenvalue problems for ordinary differential equations of fourth order with indefinite weight [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2017 We consider a nonlinearizable eigenvalue problem for the beam equation with an indefinite weight function. We investigate the structure of bifurcation set and study the behavior of connected components of the solution set bifurcating from the line of ...
Ziyatkhan Aliyev, Rada Huseynova
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Steklov problem with an indefinite weight for the p-Laplacian
Electronic Journal of Differential Equations, 2005 Let $Omegasubsetmathbb{R}^{N}$, with $Ngeq2$, be a Lipschitz domain and let 1 lees than p less than $infty$. We consider the eigenvalue problem $Delta_{p}u=0$ in $Omega$ and $| abla u|^{p-2}frac{partial u}{partial u}=lambda m|u|^{p-2}u$ on $partialOmega$
Olaf Torne
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On the fourth-order Leray–Lions problem with indefinite weight and nonstandard growth conditions
Bulletin of Mathematical Sciences, 2022 We prove the existence of at least three weak solutions for the fourth-order problem with indefinite weight involving the Leray–Lions operator with nonstandard growth conditions.
K. Kefi +3 more
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