1,720,975 research outputs found
An asymptotically linear non-cooperative elliptic system with lack of compactness
No full textIn this paper we consider an asymptotically linear, non-cooperative elliptic system at resonance. The functional associated to the system is strongly indefinite and so the Morse index of each critical point is infinite. To overcome this difficulty, we will use Morse theory for strongly indefinite functionals developed by Abbondandolo. We shall prove that, if the system has a non-resonant solution, the 'Morse index' of which is different from the 'Morse index' at infinity, then there exists another solution
Interior spikes of a singularly perturbed Neumann problem with potentials
No full textAbstractIn this paper, we prove that a singularly perturbed Neumann problem with potentials admits the existence of interior spikes concentrating in maxima and minima of an auxiliary functional depending only on the potentials
Positive energy static solutions for the Chern–Simons–Schrödinger system under a large-distance fall-off requirement on the gauge potentials
Full text linkIn this paper we prove the existence of a positive energy static solution for the Chern–Simons–Schrödinger system under a large-distance fall-off requirement on the gauge potentials. We are also interested in existence of ground state solutions
On Some Scalar Field Equations with Competing Coefficients
No full textThis paper deals with semilinear elliptic problems of the type −Δu + α(x)u = β(x)|u|p−1u in RN, u(x) >0 inRN, u ∈ H1(RN), where p is superlinear but subcritical and the coefficients α and β are positive functions such that α(x) → a∞ > 0 and β(x) → b∞ > 0, as |x| → ∞. Aim of this work is to describe some phenomena that can occur when the coefficients are “competing.
Locating the peaks of semilinear elliptic systems
No full textWe consider a system of weakly coupled singularly perturbed semilinear elliptic equations.
First, we obtain a Lipschitz regularity result for the associated ground energy function Σ
as well as representation formulas for the left and the right derivatives. Then, we show that
the concentration points of the solutions locate close to the critical points of Σ in the sense
of subdifferential calculu
Infinitely many positive solutions for a SchrdingerPoisson system
No full textWe are interested in the existence of infinitely many positive solutions of the SchrdingerPoisson system -Δu+u+V(|x|)φu=|u|p-1u, x∈R3,-Δφ=V(|x|)u2,x∈R3, where V(|x|) is a positive bounded function, 1<5 and V(r), r=|x|, has the following decay property: V(r)=arm+O(1rm+θ) with a>0, m>32, θ>0. The solutions obtained are non-radial. © 2011 Elsevier Ltd. All rights reserved
Infinitely many positive solutions for a Schrödinger-Poisson system
No full textWe are interested in the existence of infinitely many positive non-radial solutions of a Schrödinger-Poisson system with a positive radial bounded external potential decaying at infinity. © 2011 Elsevier Ltd. All rights reserved
On a class of singularly perturbed elliptic equations in divergence form: existence and multiplicity results
No full textAbstractThe main purpose of this paper is to study the existence of single-peaked positive solutions of the singularly perturbed elliptic equation -ε2div(J(x)∇u)+V(x)u=f(u)inRN,where J is a symmetric uniformly elliptic matrix and V is a positive potential, possibly unbounded from above. If f(u)=up, then solutions concentrate at non-degenerate critical points of Γ(x)=V(x)p+1p-1-N2 (detJ(x))1/2
A multiplicity result for Chern–Simons–Schrödinger equation with a general nonlinearity
No full textIn this paper we give a multiplicity result for the following Chern–Simons–Schrödinger equation (Formula presented.),where (Formula presented.), under very general assumptions on the nonlinearity g. In particular, for every n∈N, we prove the existence of (at least) n distinct solutions, for every q∈(0,qn), for a suitable qn
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