Results 51 to 60 of about 20,112 (145)
Nonhomogeneous Hemivariational Inequalities with Indefinite Potential and Robin Boundary Condition
Journal of Optimization Theory and Applications, 2017 We consider a nonlinear, nonhomogeneous Robin problem with an indefinite potential and a nonsmooth primitive in the reaction term. In fact, the right-hand side of the problem (reaction term) is the Clarke subdifferential of a locally Lipschitz integrand. We assume that asymptotically this term is resonant with respect the principal eigenvalue (from the
Nikolaos S. Papageorgiou +2 more
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Infinitely many solutions for Kirchhoff equations with indefinite potential
, 2023 We obtain a sequence of solutions converging to zero for the Kirchhoff equation $$-\left( 1+\int_Ω\left\vert \nabla u\right\vert^2\right) Δu+V(x)u=f(u)\text{,\qquad}u\in H_{0}^{1}(Ω)$$ via truncating technique and a variant of Clark's theorem due to Liu--Wang, where $Ω$ is a bounded smooth domain $Ω\subset\mathbb{R}^N$.
Jiang, Shuai, Liu, Shibo
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Semiclassical states for non-cooperative singularly perturbed fractional Schrödinger systems
Boundary Value Problems, 2022 We study the following non-cooperative type singularly perturbed systems involving the fractional Laplacian operator: { ε 2 s ( − Δ ) s u + a ( x ) u = g ( v ) , in R N , ε 2 s ( − Δ ) s v + a ( x ) v = f ( u ) , in R N , $$ \textstyle\begin{cases ...
Suhong Li +3 more
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Lifshitz tails for Anderson models with sign‐indefinite single‐site potentials [PDF]
Mathematische Nachrichten, 2015 We study the spectral minimum and Lifshitz tails for continuum random Schrödinger operators of the form urn:x-wiley:0025584X:media:mana201300160:mana201300160-math-0001where V0 is the periodic potential, are i.i.d random variables and u is the sign‐indefinite impurity potential.
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Multiple solutions with sign information for Robin equations with indefinite potential
Bulletin of Mathematical SciencesIn this paper, we study a Robin boundary value problem driven by the Laplace operator plus an indefinite potential term. The reaction is of the logistic type.
Nikolaos S. Papageorgiou +2 more
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Resonant semilinear Robin problems with a general potential
Electronic Journal of Qualitative Theory of Differential Equations, 2017 We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential. The reaction term is a Carath\'eodory function which is resonant with respect to any nonprincipal eigenvalue both at $\pm \infty$ and 0.
Nikolaos Papageorgiou +2 more
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Existence of Multiple Nontrivial Solutions for a Strongly Indefinite Schrödinger-Poisson System
Abstract and Applied Analysis, 2014 We consider a Schrödinger-Poisson system in ℝ3 with a strongly indefinite potential and a general nonlinearity. Its variational functional does not satisfy the global linking geometry.
Shaowei Chen, Liqin Xiao
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Advanced Nonlinear Studies, 2020 The aim of this paper is analyzing the positive solutions of the quasilinear ...
López-Gómez Julián, Omari Pierpaolo
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Nonlinear Neumann problems with indefinite potential and concave terms
Communications on Pure and Applied Analysis, 2015 In this paper, the authors study the following nonlinear parametric Neumann problems \[ \begin{cases} -\mathrm{div} a(Du(z))+\beta (z)|u(z)|^{p-2}u(z)=\lambda|u(z)|^{q-2}u(z)+f(z, u(z))&\text{in } \Omega,\\ \frac{\partial u}{\partial n}=0& \text{on }\partial\Omega,\end{cases}\tag{1} \] where \(\Omega \) is a bounded domain of \(\mathbb R^N\) with a \({\
Hu, Shouchuan, Papageorgiou, Nikolaos S.
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Multiple solutions for an indefinite Kirchhoff-type equation with sign-changing potential
Electronic Journal of Differential Equations, 2015 In this article, we study a Kirchhoff-type equation with sign-changing potential on an infinite domain. Using Morse theory and variational methods, we show the existence of two and of infinitely many nontrivial solutions.
Hongliang Liu, Haibo Chen
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