Results 51 to 60 of about 9,155,817 (192)
Standing waves for quasilinear Schrödinger equations with indefinite potentials
Journal of Differential Equations, 2018 We consider quasilinear Schrödinger equations in $\mathbb{R}^{N}$ of the form% \[ -Δu+V(x)u-uΔ(u^{2})=g(u)\text{,}% \] where $g(u)$ is $4$-superlinear. Unlike all known results in the literature, the Schrödinger operator $-Δ+V$ is allowed to be indefinite, hence the variational functional does not satisfy the mountain pass geometry.
Shibo Liu, Jian Zhou
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Kirchhoff type problems with potential well and indefinite potential
Electronic Journal of Differential Equations, 2016 In this article, we study the Kirchhoff type problem $$\displaylines{ -\Big(\alpha\int_{\mathbb{R}^3}|\nabla u|^2dx+1\Big)\Delta u +(\lambda a(x)+a_0)u=|u|^{p-2}u \quad\text{in }\mathbb{R}^3,\cr u\in H^1(\mathbb{R}^3), }$$ where ...
Yuanze Wu, Yisheng Huang, Zeng Liu
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About the whereabouts of indefinites [PDF]
, 2013 The paper characterizes three different domains in the German middle field which are relevant for the interpretation of an indefinite. It is argued that the so-called 'strong' reading of an indefinite is the basic one and that the 'weak' reading needs ...
Frey, Werner
core
Variational Estimates for Discrete Schr�dinger Operators with Potentials of Indefinite Sign [PDF]
Communications in Mathematical Physics, 2003 17 ...
Damanik, D. +3 more
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Existence of solutions to quasilinear Schrodinger equations with indefinite potential
Electronic Journal of Differential Equations, 2015 In this article, we study the existence and multiplicity of solutions of the quasilinear Schrodinger equation $$ -u''+V(x)u-(|u| ^2)''u=f(u) $$ on $\mathbb{R}$, where the potential $V$ allows sign changing and the nonlinearity satisfies conditions
Zupei Shen, Zhiqing Han
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 In this paper we are concerned with the study of the spectrum for a class of eigenvalue problems driven by two non-homogeneous differential operators with different variable growth and an indefinite potential in the following ...
Uţă Vasile-Florin
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Advances in Mathematical Physics, 2020 In this paper, we show the existence of solutions for an indefinite fractional Schrödinger equation driven by the variable-order fractional magnetic Laplace operator involving variable exponents and steep potential.
Jianwen Zhou +3 more
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Positive bounded solutions for semilinear elliptic systems with indefinite weights in the half-space
Electronic Journal of Differential Equations, 2015 In this article, we study the existence and nonexistence of positive bounded solutions of the Dirichlet problem $$\displaylines{ -\Delta u=\lambda p(x)f(u,v),\quad \text{in } {\mathbb{R}}_+^n,\cr -\Delta v=\lambda q(x)g(u,v), \quad \text{in ...
Ramzi Alsaedi +3 more
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An existence result for a Robin problem involving $p(x)$-Kirchhoff-type equation with indefinite weight [PDF]
AUT Journal of Mathematics and ComputingThis paper discusses the existence of at least two distinct nontrivial weak solutions for a class of $p(x)$-Kirchhoff-type equation plus an indefinite potential under Robin boundary condition.
Mehdi Latifi, Mohsen Alimohammady
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Galaxies, 2020 Higher dimensional theories, wherein our four dimensional universe is immersed into a bulk ambient, have received much attention recently, and the directions of investigation had, as far as we can discern, all followed the ordinary Euclidean hypersurface
Fan Zhang
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