### Giovanna Cerami

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## Pubblicazioni

*Il seguente elenco è solo una parte della Produzione scientifica del docente.*

Per maggiori informazioni consultare il Catalogo Istituzionale dei prodotti della Ricerca (IRIS) .

Cerami Giovanna and Pomponio Alessio.

**On Some Scalar Field Equations with Competing Coefficients**. 2015. BibTeX@misc{ 11589_60474, author = "Cerami Giovanna and Pomponio Alessio", title = "On Some Scalar Field Equations with Competing Coefficients", year = 2015 }

Cerami G, Zhong X and Zou W.

**On some nonlinear PDEs with Sobolev-hardy critical exponents and a Li-Lin open problem**.*CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS*54:1793–1829, 2015. URL, DOI BibTeX@article{ 11589_1396, author = "Cerami G and Zhong X and Zou W", title = "On some nonlinear PDEs with Sobolev-hardy critical exponents and a Li-Lin open problem", year = 2015, journal = "CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS", volume = 54, abstract = "Let Ω be a C1 open bounded domain in ℝN, N ≥ 3, with (Formula presented.). We consider the following problem involving Hardy–Sobolev critical exponents: (Formula presented.), where 0 ≤ s1 < 2, 0 ≤ s2 < 2, 2 *(s2) ≠ λ ∈ ℝ, 1 ≤ p ≤ 2*(s1) - 1 and with choices of exponents and parameters corresponding to cases in which (P) has not been before investigated. We prove the existence of positive solutions, which, in some cases, are also shown to be ground states. We remark that we give a first partial answer to a question proposed by Li and Lin (Arch Ration Mech Anal 203(3):943–968, 2012). © 2015, Springer-Verlag Berlin Heidelberg.", keywords = "Hardy-Sobolev critical exponent, Li-Lin open problem, positive solutions, variational methods.", url = "http://download.springer.com/static/pdf/716/art%253A10.1007%252Fs00526-015-0844-z.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2Fs00526-015-0844-z&token2=exp=1450193778~acl=%2Fstatic%2Fpdf%2F716%2Fart%25253A10.1007%25252Fs00526-015-0844-z.pdf%3ForiginUrl%3Dhttp%253A%252F%252Flink.springer.com%252Farticle%252F10.1007%252Fs00526-015-0844-z*~hmac=3c143056d9dfe9c2d9e4a68e9e74aa6c4bc3d0f2beba69aefc45030729f9b462", doi = "10.1007/s00526-015-0844-z", pages = "1793--1829" }

Bartolo Rossella, Capozzi Alberto, Cerami Giovanna, Cingolani Silvia, D’Avenia Pietro, Greco Carlo, Palagachev Dian, Pomponio Alessio and Vannella Giuseppina.

**Variational methods in the study of nonlinear problems and applications**. In*I gruppi di ricerca sfide tecnologiche e sociali*B. 2014, 179–183. BibTeX@conference{ 11589_60293, author = "Bartolo Rossella and Capozzi Alberto and Cerami Giovanna and Cingolani Silvia and D’Avenia Pietro and Greco Carlo and Palagachev Dian and Pomponio Alessio and Vannella Giuseppina", title = "Variational methods in the study of nonlinear problems and applications", year = 2014, publisher = "Gangemi Editore spa", address = "Roma", volume = "B", booktitle = "I gruppi di ricerca sfide tecnologiche e sociali", abstract = "In this paper we illustrate the lineguides of our research group. We describe some recent results concerning the study of some nonlinear differential equations and systems having a variational nature and arising from physics, geometry and applied sciences. In particular we report existence, multiplicity and regularity results for the solutions of these nonlinear problems. We point out that, in treating the above problems, the used methods for finding solutions are variational and topological, indeed the existence of solutions of the considered equations is obtained searching for critical points of suitable functionals defined on manifolds embedded into infinite dimensional functional spaces, while the regularity of the solutions is studied by means of geometric and harmonic analysis tools.", keywords = "Nonlinear Partial Differential Equations, Solutions, Existence, Multiplicity, Regularity", pages = "179--183" }

CERAMI G, MOLLE R and PASSASEO D.

**Multiplicity of Positive and Nodal Solutions for Scalar Field Equations**.*JOURNAL OF DIFFERENTIAL EQUATIONS*257:3554–3606, 2014. URL, DOI BibTeX@article{ 11589_1570, author = "CERAMI G and MOLLE R and PASSASEO D", title = "Multiplicity of Positive and Nodal Solutions for Scalar Field Equations", year = 2014, journal = "JOURNAL OF DIFFERENTIAL EQUATIONS", volume = 257, abstract = "In this paper the question of finding infinitely many solutions to the problem $−\Delta u +a(x)u =|u|^{p−2}u$ , in $R^N$, u ∈H^1(R^N), is considered when N≥2, p∈(2, 2N/(N−2)), and the potential a(x) is a positive function which is not required to enjoy symmetry properties. Assuming that a(x)satisfies a suitable “slow decay at infinity” condition and, moreover, that its graph has some “dips”, we prove that the problem admits either infinitely many nodal solutions orinfinitely many constant sign solutions. The proof method is purely variational and allows to describe the shape of the solutions.", keywords = "Scalar field equations, multiple positive and nodal solutions, nonsymmetric coefficients.", url = "http://adsabs.harvard.edu/abs/2014JDE...257.3554C", doi = "10.1016/j.jde.2014.07.002", pages = "3554--3606" }

CERAMI G.

. Volume 85, pages 207–230, BIRKHAUSER, 2014. URL, DOI BibTeX**Existence and Multiplicity Results for Some Scalar Fields Equations**@inbook{ 11589_14755, author = "CERAMI G", title = "Existence and Multiplicity Results for Some Scalar Fields Equations", year = 2014, publisher = "BIRKHAUSER", address = "Basel", journal = "PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS", volume = 85, booktitle = "Analysis and Topology in Nonlinear Differential Equations", abstract = "In this paper the results of some researches concerning scalar field equations are summarized. The interest is focused on the question of existence and multiplicity of stationary solutions; so the model equation $-\Delta u + a(x)u = |u|^{p-1}u$ in $\real^N$, is considered. The difficulties and the ideas introduced to face them as well as known results are discussed. Some recent advances concerning existence and multiplicity of multi-bump solutions are described in detail. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM.", keywords = "Elliptic equation in R^N, variational methods, multibump solutions, infinitely many positive and nodal solutions.", url = "http://www.springer.com/gp/book/9783319042138", doi = "10.1007/978-3-319-04214-5", pages = "207--230" }

Cerami G, Passaseo D and Solimini S.

**Nonlinear scalar field equations: Existence of a positive solution with infinitely many bumps**.*ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE*32:23–40, 2013. URL, DOI BibTeX@article{ 11589_5566, author = "Cerami G and Passaseo D and Solimini S", title = "Nonlinear scalar field equations: Existence of a positive solution with infinitely many bumps", year = 2013, journal = "ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE", volume = 32, abstract = {In this paper we consider the equation {equation presented}. During last thirty years the question of the existence and multiplicity of solutions to (E) has been widely investigated mostly under symmetry assumptions on a. The aim of this paper is to show that, differently from those found under symmetry assumption, the solutions found in [6] admit a limit configuration and so (E) also admits a positive solution of infinite energy having infinitely many "bumps".}, keywords = "Schrödinger equation; Solutions with infinitely many bumps; Variational methods", url = "http://adsabs.harvard.edu/abs/2015AnIHP..32...23C", doi = "10.1016/j.anihpc.2013.08.008", pages = "23--40" }

Cerami G, Passaseo D and Solimini S.

**Infinitely many positive solutions to some scalar field equations with non-symmetric coefficients**.*COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS*66:372–413, 2013. URL, DOI BibTeX@article{ 11589_52331, author = "Cerami G and Passaseo D and Solimini S", title = "Infinitely many positive solutions to some scalar field equations with non-symmetric coefficients", year = 2013, journal = "COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS", volume = 66, abstract = "In this paper the equation $ -\Delta u+a(x)u=|u|^{p-1}u \mbox{ in }\R^N$ is considered, when $N \ge2$, $p>1,\ p<{\frac{N+2}{N-2}},$ if $N\ge 3.$ Assuming that the potential $a(x)$ is a positive function belonging to $L^{N/2}_ {loc}(\R^N),$ such that $a(x)\to a_\infty > 0, \ \mbox{as} \ |x|\rightarrow \infty$, and that satisfies slow decay assumptions, but not requiring any symmetry property, the existence of infinitely many positive solutions, by purely variational methods, is proved. The shape of the solutions is described and, furthermore, their asymptotic behavior when $|a(x) - a_\infty|_ {L^ {N/2}_ {loc}(\R^N)} \to 0$.", keywords = "Schroedinger equations, infinitely many positive solutions, nonsymmetric coefficients", url = "http://onlinelibrary.wiley.com/doi/10.1002/cpa.21410/abstract", doi = "10.1002/cpa.21410", pages = "372--413" }

Cerami G and Vaira G.

**Positive solutions for some non autonomous Schrodinger-Poisson Systems**.*JOURNAL OF DIFFERENTIAL EQUATIONS*248:521–543, 2010. DOI BibTeX@article{ 11589_8972, author = "Cerami G and Vaira G", title = "Positive solutions for some non autonomous Schrodinger-Poisson Systems", year = 2010, journal = "JOURNAL OF DIFFERENTIAL EQUATIONS", volume = 248, abstract = "vedi allegato", doi = "10.1016/j.jde.2009.06.017", pages = "521--543" }

CERAMI G and MOLLE R.

**On some Schroedinger equations with non regular potential at infinity**.*DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS*28:827–844, 2010. BibTeX@article{ 11589_9480, author = "CERAMI G and MOLLE R", title = "On some Schroedinger equations with non regular potential at infinity", year = 2010, journal = "DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS", volume = 28, abstract = "vedi allegato", pages = "827--844" }

Cerami G and Molle R.

**Positive solutions for some Schrodinger equations having partially periodic potentials**.*JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS*359:15–27, 2009. DOI BibTeX@article{ 11589_6552, author = "Cerami G and Molle R", title = "Positive solutions for some Schrodinger equations having partially periodic potentials", year = 2009, journal = "JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS", volume = 359, keywords = "Lack of compactness; Multiplicity of positive solutions; Nonautonomous problems; Schrödinger equation", doi = "10.1016/j.jmaa.2009.05.011", pages = "15--27" }

CANDELA A, CERAMI G and PALMIERI G.

**On some non homogeneous elliptic problems in unbounded domains**.*ADVANCED NONLINEAR STUDIES*9:625–637, 2009. BibTeX@article{ 11589_9361, author = "CANDELA A and CERAMI G and PALMIERI G", title = "On some non homogeneous elliptic problems in unbounded domains", year = 2009, journal = "ADVANCED NONLINEAR STUDIES", volume = 9, abstract = "vedi allegato", pages = "625--637" }