951 research outputs found
Concentration and compactness in nonlinear Schrodinger-Poisson system with a general nonlinearity
In this paper we use a concentration and compactness argument to prove the
existence of a nontrivial nonradial solution to the nonlinear
Schrodinger-Poisson equations in R3, assuming on the nonlinearity the general
hypotheses introduced by Berestycki & LionsComment: 22 page
On a "zero mass" nonlinear Schrodinger equation
We look for positive solutions to the nonlinear Schrodinger equation with a
potential, under the hypothesis of zero mass on the nonlinearity, in a
particular situation. Existence and multiplicity results are provided.Comment: 32 pages. We corrected a gap in the proof of Theorem 3.
Compactness results and applications to some "zero mass" elliptic problems
In this paper we present some compactness results, showing how they can be
applied in dealing with "zero mass" problems by a variational approach. In
particular we use our results in two different situations: we look for complex
valued solutions of a very classical elliptic equation, and we study an
elliptic problem on an axially symmetric unbounded domain.Comment: 28 page
On the Schrodinger equation in under the effect of a general nonlinear term
In this paper we prove the existence of a positive solution to the equation
in assuming the general hypotheses on the
nonlinearity introduced by Berestycki & Lions. Moreover we show that a
minimizing problem, related to the existence of a ground state, has no
solution.Comment: 18 page
Generalized Schr\"odinger-Newton system in dimension : critical case
In this paper we study a system which is equivalent to a nonlocal version of
the well known Brezis Nirenberg problem. The difficulties related with the lack
of compactness are here emphasized by the nonlocal nature of the critical
nonlinear term. We prove existence and nonexistence results of positive
solutions when and existence of solutions in both the resonance and the
nonresonance case for higher dimensions.Comment: 18 pages, typos fixed, some minor revision
- …