1,721,101 research outputs found
A local mountain pass approach for a class of fractional NLS equations with magnetic fields
No full textConcentrating solutions for a class of nonlinear fractional Schrödinger equations in RN
No full textWe deal with the existence of positive solutions for the following fractional Schrödinger equation: ε2s(−Δ)su + V (x)u = f(u) in RN , where ε > 0 is a parameter, s ∈ (0, 1), N ≥ 2, (−Δ)s is the fractional Laplacian operator, and V : RN → R is a positive continuous function. Under the assumptions that the nonlinearity f is either asymptotically linear or superlinear at infinity, we prove the existence of a family of positive solutions which concentrates at a local minimum of V as ε tends to zero
Multiplicity and concentration of solutions for fractional Schrödinger systems via penalization method
No full textA strong maximum principle for the fractional (p,q)-Laplacian operator
No full textIn this note, we prove a strong maximum principle for weak supersolutions of (−Δ)psu+(−Δ)qsu+c(x)(|u|p−2u+|u|q−2u)=0 in Ω, where Ω⊂RN is an open set, s∈(0,1), 1<∞, c∈C(Ω ̄), and (−Δ)ts, with t∈{p,q}, is the fractional t-Laplacian operator
Infinitely many small energy solutions for a fractional Kirchhoff equation involving sublinear nonlinearities
No full textThis article is devoted to the study of the following fractional Kirchhoff equation (Formula presented) where (−∆)s is the fractional Laplacian, M: R+ → R+ is the Kirchhoff term, V: RN → R is a positive continuous potential and f(x, u) is only locally defined for |u| small. By combining a variant of the symmetric Mountain Pass with a Moser iteration argument, we prove the existence of infinitely many weak solutions converging to zero in L∞(RN )-norm
Existence and concentration results for some fractional Schrödinger equations in R^N with magnetic fields
No full textWe consider some nonlinear fractional Schrödinger equations with magnetic field and involving continuous nonlinearities having subcritical, critical or supercritical growth. Under a local condition on the potential, we use minimax methods to investigate the existence and concentration of nontrivial weak solutions
Multiplicity and concentration results for a class of critical fractional Schrödinger-Poisson systems via penalization method
Full text linkWe deal with the multiplicity and concentration of positive solutions for the following fractional Schrödinger-Poisson-type system with critical growth: (equation required), where > 0 is a small parameter, s (3 4, 1), t (0, 1), (-Δ)α, with α {s,t}, is the fractional Laplacian operator, V is a continuous positive potential and f is a superlinear continuous function with subcritical growth. Using penalization techniques and Ljusternik-Schnirelmann theory, we investigate the relation between the number of positive solutions with the topology of the set where the potential attains its minimum valu
A multiplicity result for a fractional p-Laplacian problem without growth conditions
No full textUsing an abstract critical point result due to Ricceri and combining a truncation argument with a Moser-type iteration, we establish the existence of at least three bounded solutions for a fractional p-Laplacian problem depending on two parameters and involving nonlinearities with arbitrary growth
Concentration phenomena for a class of fractional Kirchhoff equations in RN with general nonlinearities
Full text linkIn this paper we study the following class of fractional Kirchhoff problems: ε2sM(ε2s−N[u]s2)(−Δ)su+V(x)u=f(u) in RN,u∈Hs(RN),u>0 in RN,where ε>0 is a small parameter, s∈(0,1), N≥2, (−Δ)s is the fractional Laplacian, V:RN→R is a positive continuous function, M:[0,∞)→R is a Kirchhoff function satisfying suitable conditions and f:R→R fulfills Berestycki–Lions type assumptions of subcritical or critical type. Using suitable variational arguments, we prove the existence of a family of positive solutions (uε) which concentrates at a local minimum of V as ε→0
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