In this paper we show an abstract theorem involving the existence of critical points for a functional I, which permit us to prove the existence of solutions for a large class of Berestycki-Lions type problems. In the proof of the abstract result we apply the deformation lemma on a special set associated with I, which we call of Pohozaev set.2010 Mathematics Subject Classification. 35J60; 35A15, 49J52.

It is well known that, in the context of general relativity, an unknown kind of matter that must violate the strong energy condition is required to explain the current accelerated phase of expansion of the Universe. This unknown component is called dark energy and is characterized by an equation of state parameter w = p/ρ < −1/3. Thermodynamic stability requires that 3w − d ln |w|/d ln a ≥ 0 and positiveness of entropy that w ≥ −1. In this paper we proof that we cannot obtain a differentiable function w(a) to represent the dark energy that satisfies these conditions trough the entire history of the Universe.PACS numbers: 98.80. Es, 98.80.Jk

In this paper, we investigate the existence of nonnegative solutions for the problemis a integro-differential operator with measurable kernel K and V is a continuous potential. Under apropriate hypothesis, we prove, using variational methods, that the above equation has solution.

In this paper we investigate the existence of positive solutions and ground state solutions for a class of fractional Schrödinger-Poisson equations in R 3 with general nonlinearity.

No abstract