Results 11 to 20 of about 91,659 (256)
Mathematical Modelling and Analysis, 2006 We establish the existence of an entire solution for a class of stationary Schrodinger systems with subcritical discontinuous nonlinearities and lower bounded potentials that blow‐up at infinity.
T. L. Dinu
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Sign-changing solutions for critical equations with Hardy potential [PDF]
Analysis & PDE, 2021 41 pages, Updated version - if any - can be downloaded at http://www.birs.ca/~nassif/
Esposito P. +3 more
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Multiple solutions for quasilinear elliptic equations with sign-changing potential
Electronic Journal of Differential Equations, 2016 In this article, we study the quasilinear elliptic equation $$ -\Delta_{p} u-(\Delta_{p}u^{2})u+ V (x)|u|^{p-2}u=g(x,u), \quad x\in \mathbb{R}^N, $$ where the potential V(x) and the nonlinearity g(x,u) are allowed to be sign-changing.
Ruimeng Wang, Kun Wang, Kaimin Teng
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Infinitely many solutions for quasilinear Schrödinger equation with general superlinear nonlinearity
Boundary Value Problems, 2023 In this article, we study the quasilinear Schrödinger equation − △ ( u ) + V ( x ) u − △ ( u 2 ) u = g ( x , u ) , x ∈ R N , $$ -\triangle (u)+V(x)u-\triangle \bigl(u^{2}\bigr)u=g(x,u), \quad x\in \mathbb{R}^{N}, $$ where the potential V ( x ) $V(x)$ and
Jiameng Li +3 more
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Ground state sign-changing solutions for critical Choquard equations with steep well potential
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper, we study sign-changing solution of the Choquard type equation \begin{align*} -\Delta u+\left(\lambda V(x)+1\right)u =\big(I_\alpha\ast|u|^{2_\alpha^*}\big)|u|^{2_\alpha^*-2}u +\mu|u|^{p-2}u\quad \mbox{in}\ \mathbb{R}^N, \end{align*} where
Yong-Yong Li, Gui-Dong Li, Chun-Lei Tang
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PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL [PDF]
Bulletin of the Australian Mathematical Society, 2010 AbstractIn this paper we study the existence of positive periodic solutions to second-order singular differential equations with the sign-changing potential. Both the repulsive case and the attractive case are studied. The proof is based on Schauder’s fixed point theorem. Recent results in the literature are generalized and significantly improved.
Chu, Jifeng, Zhang, Ziheng
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On the existence and multiplicity of solutions for nonlinear Klein–Gordon–Maxwell system
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we study the existence and multiplicity solutions for the following Klein–Gordon–Maxwell system \begin{align*} \begin{cases} - \Delta u +V(x)u-(2\omega+\phi)\phi u =f(x,u), &x\in \mathbb{R}^3,\\ \Delta \phi =(\omega+\phi)u^2, \quad &
Lixia Wang +2 more
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On Landis’ conjecture in the plane for some equations with sign-changing potentials [PDF]
Revista Matemática Iberoamericana, 2020 In this article, we investigate the quantitative unique continuation properties of real-valued solutions to elliptic equations in the plane. Under a general set of assumptions on the operator, we establish quantitative forms of Landis’ conjecture. Of note, we prove a version of Landis’ conjecture for solutions to
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Wegner Estimates for Sign-Changing Single Site Potentials [PDF]
Mathematical Physics, Analysis and Geometry, 2010 We study Anderson and alloy type random Schrödinger operators on $\ell^2(\ZZ^d)$ and $L^2(\RR^d)$. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. For a certain class of models we prove a Wegner estimate which is linear in the volume of the box and the length
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On a class of superlinear nonlocal fractional problems without Ambrosetti–Rabinowitz type conditions
Electronic Journal of Qualitative Theory of Differential Equations, 2019 In this note, we deal with the existence of infinitely many solutions for a problem driven by nonlocal integro-differential operators with homogeneous Dirichlet boundary conditions \begin{equation*} \begin{cases} -\mathcal{L}_{K}u=\lambda f(x,u), &
Qing-Mei Zhou
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