129 research outputs found
On the fractional Schr\"{o}dinger-Kirchhoff equations with electromagnetic fields and critical nonlinearity
We consider the fractional Schr\"{o}dinger-Kirchhoff equations with
electromagnetic fields and critical nonlinearity
where as and
is the fractional magnetic operator with , is a continuous nondecreasing
function, and are the electric and the magnetic potential,
respectively. By using the fractional version of the concentration compactness
principle and variational methods, we show that the above problem: (i) has at
least one solution provided that ; and (ii) for any
, has pairs of solutions if , where and are
sufficiently small positive numbers. Moreover, these solutions as
Sign-changing solutions for fourth-order elliptic equations of Kirchhoff type with critical exponent
Global existence and blow-up for semilinear parabolic equation with critical exponent in RN
In this paper, we use the self-similar transformation and the modified potential well method to study the long time behaviors of solutions to the classical semilinear parabolic equation associated with critical Sobolev exponent in RN. Global existence and finite time blowup of solutions are proved when the initial energy is in three cases. When the initial energy is low or critical, we not only give a threshold result for the global existence and blowup of solutions, but also obtain the decay rate of the L 2 norm for global solutions. When the initial energy is high, sufficient conditions for the global existence and blowup of solutions are also provided. We extend the recent results which were obtained in [R. Ikehata, M. Ishiwata, T. Suzuki, Ann. Inst. H. Poincaré Anal. Non Linéaire 27(2010), No. 3, 877– 900]
p-fractional Hardy–Schrödinger–Kirchhoff systems with critical nonlinearities
Abstract
This paper deals with the existence of nontrivial solutions for critical Hardy–Schrödinger–Kirchhoff
systems driven by the fractional p-Laplacian operator. Existence is derived
as an application of the mountain pass theorem and the Ekeland variational principle.
The main features and novelty of the paper are the presence of the Hardy terms as well as critical nonlinearities
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