INdAM - GNAMPA Project 2015

Modelli ed equazioni non-locali di tipo frazionario

 

Principal investigator:

- Giovanni Molica Bisci (Università ‘Mediterranea’ di Reggio Calabria)





Workshops and conferences:

- Advances in Game Theory, Università ‘Mediterranea’ di Reggio Calabria, May 7, 2015

- Mathematical Analysis, Modelling and Applications, Università ‘Mediterranea’ di Reggio Calabria, June 5, 2015

- Two nonlinear days in Urbino, Università degli Studi di Urbino 'Carlo Bo', July 2-3, 2015

- 2nd Conference on Recent Trends in Nonlinear Phenomena, Università degli Studi di Napoli 'Parthenope', November 4-6, 2015

- Una Giornata sulle Equazioni Ellittiche Nonlineari, Università degli Studi di Perugia, January 13, 2016





Visiting professors:

- Xavier Cabré, ICREA and Universitat Polytècnica de Catalunya, Spain

- Vicentiu Radulescu, University of Craiova and Romanian Academy, Romania




Talks:

- R. Bartolo, Recent results on p-asymptotically linear problems, at the Conference on Partial Differential Equations at the Technische Universitat Munchen, Munchen, Germany, March 25-29, 2015;

- R. Bartolo, A pseudo-index approach to fractional equations, at the Departemento de Algebra, Geometria y Topologia, Malaga University, Spain, April 13, 2015;

- G. Molica Bisci, Recent trends on fractional equations, at the Conference on Partial Differential Equations at the Technische Universitat Munchen, Munchen, Germany, March 25-29, 2015;

- R. Servadei, On some equations in a nonlocal fractional setting, at the Conference on Partial Differential Equations at the Technische Universitat Munchen, Munchen, Germany, March 25-29, 2015;

- G. Molica Bisci, A Brezis-Nirenberg type result for a nonlocal fractional operator, at the Una Giornata sulle Equazioni Ellittiche Nonlineari at the Università degli Studi di Perugia, Italy, January 13, 2016;

- R. Servadei, Critical fractional equations with concave-convex nonlinearities, at the Una Giornata sulle Equazioni Ellittiche Nonlineari at the Università degli Studi di Perugia, Italy, January 13, 2016.




Publications:

- G. Afrouzi - A. Hadjian - G. Molica Bisci: ‘Some remarks for one-dimensional mean curvature problems through a local minimization principle’, Adv. Nonlinear Anal., 2 (2013), no. 4, 427–441;

- G. Afrouzi - A. Hadjian - G. Molica Bisci: ‘A variational approach for one-dimensional prescribed mean curvature problems’, J. Aust. Math. Soc., 97 (2014), no. 2, 145–161;

- B. Barrios - E. Colorado - R. Servadei - F. Soria: ‘A critical fractional equation with concave-convex power nonlinearities’, Ann. Inst. H. Poincaré Anal. Non Linéaire, 32 (2015), 875-900;

- R. Bartolo: ‘ Multiplicity results for a class of quasilinear elliptic problems’, Mediterr. J. Math., DOI 10.1007/s00009-013-0378-6;

- R. Bartolo - A.M. Candela - J.L. Flores: ‘Connection by geodesics on globally hyperbolic spacetimes with a lightlike Killing vector field’, preprint del Dipartimento di Matematica dell'Università degli Studi di Bari 2014, arXiv:1405.0804, Rev. Mat. Iberoam., in press;

- R. Bartolo - A.M. Candela - J.L. Flores: ‘Connection by geodesics on open subsets of globally hyperbolic spacetimes, International Journal of Geometric Methods in Modern Physics, in press;

- R. Bartolo - A.M. Candela - A. Salvatore: ‘Multiplicity results for a class of asymptotically p-linear equations on \(R^N\)’, Comm. Contemp. Math., in press;

- R. Bartolo - A.M. Candela - A. Salvatore: ‘Infinitely many solutions for a perturbed Schrdinger equation, preprint;

- R. Bartolo - G. Molica Bisci: ‘A pseudo-index approach to fractional equations’, Expo. Math., 33 (2015), no. 4, 502–516;

- Z. Binlin - G. Molica Bisci - R. Servadei: ‘Superlinear nonlocal fractional problems with infinitely many solutions, Nonlinearity, 28 (2015), no. 7, 2247–2264;

- M. Ferrara - G. Molica Bisci: ‘Existence results for elliptic problems with Hardy potential’, Bull. Sci. Math., 138 (2014), no. 7, 846–859;

- M. Ferrara - G. Molica Bisci: ‘Remarks for one-dimensional fractional equations’, Opuscula Math., 34 (2014), no. 4, 691–698;

- M. Ferrara - G. Molica Bisci - B. Zhang: ‘Existence of weak solutions for non-local fractional problems via Morse theory’, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), no. 8, 2483–2499;

- G.M. Figueiredo - G. Molica Bisci - R. Servadei: `On a fractional Kirchhoff-type equation via Krasnoselskii's genus', Asymptot. Anal., 94 (2015), 347-361;

- A. Fiscella - G. Molica Bisci - R. Servadei: ‘Bifurcation and multiplicity results for critical nonlocal fractional Laplacian problems’, Bull. Sci. Math., 140 (2016), no. 1, 14–35;

- A. Fiscella - R. Servadei - E. Valdinoci: ‘Density properties for fractional Sobolev spaces’, Ann. Acad. Sci. Fenn. Math., 40, 2015, 235-253;

- A. Greco - R. Servadei: ‘Hopf’s lemma and constrained radial symmetry for the fractional Laplacian’, Math. Res. Lett., in press;

- M. Imbesi - G. Molica Bisci: ‘Discrete elliptic Dirichlet problems and nonlinear algebraic systems’, Mediterr. J. Math., in press;

- G. Molica Bisci: ‘Fractional equations with bounded primitive’, Appl. Math. Lett., 27 (2014), 53–58;

- G. Molica Bisci - P. Pizzimenti: ‘Sequences of weak solutions for non-local elliptic problems with Dirichlet boundary condition’, Proc. Edinb. Math. Soc., (2) 57 (2014), no. 3, 779–809;

- G. Molica Bisci - V. Radulescu: ‘Mountain Pass solutions for nonlocal equations’, Ann. Acad. Sci. Fenn. Math., 39 (2014), no. 2, 579–592;

- G. Molica Bisci - V. Radulescu: ‘Applications of local Linking to nonlocal Neumann problems’, Commun. Contemp. Math., 17 (2015), no. 1, 1450001, 17 pp;

- G. Molica Bisci - V. Radulescu: ‘Bifurcation analysis of a singular elliptic problem modelling the equilibrium of anisotropic continuous media’, Topol. Methods Nonlinear Anal., in press;

- G. Molica Bisci - V. Radulescu: ‘A characterization for elliptic problems on fractal sets’, Proc. Amer. Math. Soc., 143 (2015), no. 7, 2959–2968;

- G. Molica Bisci - V. Radulescu - R. Servadei: ‘Competition phenomena for elliptic equations involving a general operator in divergence form’, Anal. Appl., in press;

- G. Molica Bisci - D. Repovs: ‘Multiple solutions for elliptic equations involving a general operator in divergence form’, Ann. Acad. Sci. Fenn. Math., 39 (2014), no. 1, 259–273;

- G. Molica Bisci - D. Repovs: ‘On sequences of solutions for discrete anisotropic equations’, Expo. Math., 32 (2014), no. 3, 284–295;

- G. Molica Bisci - D. Repovs: ‘Nonlinear Neumann problems driven by a nonhomogeneous differential operator’, Bull. Math. Soc. Sci. Math. R. S. Roumanie, in press, ISSN: 1220-3874;

- G. Molica Bisci - D. Repovs: ‘On biharmonic equations with Navier boundary conditions’, Complex Var. Elliptic Equ., in press, ISSN: 1747-6933;

- G. Molica Bisci - D. Repovs: ‘Higher nonlocal problems with bounded potential’, J. Math. Anal. Appl., 420 (2014), no. 1, 167–176;

- G. Molica Bisci - D. Repovs: ‘On doubly nonlocal fractional elliptic equations’, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 26 (2015), no. 2, 161–176;

- G. Molica Bisci - D. Repovs: ‘Existence and localization of solutions for nonlocal fractional equations’, Asymptot. Anal., 90 (2014), no. 3-4, 367–378;

- G. Molica Bisci - R. Servadei: ‘A bifurcation result for nonlocal fractional equations’, Anal. Appl.,13, no.4, 2015, 371-394;

- G. Molica Bisci - R. Servadei: ‘Lower semicontinuity of functionals of fractional type and applications to nonlocal equations with critical Sobolev exponent’, Adv. Differential Equations, 20, no.7-8, 2015, 635-660;

- G. Molica Bisci - R. Servadei: `A Brezis-Nirenberg splitting approach for nonlocal fractional problems', Nonlinear Anal., 119, 2015, 341-353.