List of Papers (March, 2017)

  • (with S. Cingolani, M. Gallo), Multiple solutions for the nonlinear Choquard equation with even or odd nonlinearities, Calc. Var. Partial Differential Equations 61 (2022), no. 2, Paper No. 68, 34.
  • (with S. Cingolani, M. Gallo), On fractional Schr\"odinger equations with Hartree type nonlinearities, Math. Eng. 4 (2022), no. 6, Paper No. 056, 33.
  • (with N. Ikoma, Z.-Q. Wang, C. Zhang), Semi-classical states for logarithmic Schr\"odinger equations, Nonlinearity 34 (2021) 1900--1942.
  • (with S. Cingolani), Deformation argument under PSP condition and applications, Anal. Theory Appl., Vol. 37, No. 2 (2021), 191--208.
  • (with S. Cingolani, M. Gallo), Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation, Nonlinearity 34 (2021), no. 6, 4017--4056.
  • (with S. Cingolani, M. Gallo), Erratum: Normalized solutions for fractional nonlinear scalar field equations via Lagrangian formulation (2021 {\it Nonlinearity} 34 4017), Nonlinearity 34 (2021), no. 10, C3.
  • (with S. Cingolani), Ground state solutions for the nonlinear Choquard equation with prescribed mass, Gometric Properties for Parabolic and Elliptic PDE (2020).
  • (with J. Hirata), Nonlinear scalar field equations with $L^2$ constraint: Mountain pass and symmetric mountain pass approaches, Adv. Nonlinear Stud., Vol. 9, Issue 2, 263--290 (2019).
  • (with N. Ikoma), A note on deformation argument for {$L^2$} normalized solutions of nonlinear Schr\"odinger equations and systems, Adv. Differential Equations 24 (2019), no. 11-12, 609--646.
  • (with S. Cingolani), Semi-classical states for the nonlinear Choquard equations: existence, multiplicity and concentration at a potential well, Rev. Mat. Iberoam. 35 (2019), no. 6, 1885--1924.
  • (with J. Hirata), Nonlinear scalar field equations with {$L^2$} constraint: mountain pass and symmetric mountain pass approaches, Adv. Nonlinear Stud. 19 (2019), no. 2, 263--290.
  • (with G. Jiang, C. Zhang), Remarks on the Clark theorem, J. Nonlinear Convex Anal. 18 (2017), no. 8, 1421--1434.
  • (with S. Cingolani, L. Jeanjean), Multiple complex-valued solutions for nonlinear magnetic Schrodinger equations. J. Fixed Point Theory Appl. 19 (2017), no. 1, 37--66.
  • (with C. Zhang), Multi-bump solutions for logarithmic Schrodinger equations. Calc. Var. Partial Differential Equations 56 (2017), no. 2, 56:33.
  • (with S. Cingolani, L. Jeanjean), Multiplicity of positive solutions of nonlinear Schrodinger equations concentrating at a potential well. Calc. Var. Partial Differential Equations 53 (2015), no. 1--2, 413--439.
  • (with D. Arcoya, C. De Coster, L. Jeanjean), Continuum of solutions for an elliptic problem with critical growth in the gradient, J. Funct. Anal. 268 (2015), no. 8, 2298 2335.
  • (with D. Arcoya, C. De Coster, L. Jeanjean), Remarks on the uniqueness for quasilinear elliptic equations with quadratic growth conditions. J. Math. Anal. Appl. 420 (2014), no. 1, 772 780.
  • (with C.-N. Chen), A variational approach for standing waves of FitzHugh-Nagumo type systems. J. Differential Equations 257 (2014), no. 1, 109 144.
  • (with J. Byeon), Multi-bump positive solutions for a nonlinear elliptic problem in expanding tubular domains, Calc. Var. Partial Differential Equations 50 (2014), no. 1--2, 365--397.
  • (with N. Hayashi, T. Ozawa), On a system of nonlinear Schr\"{o}dinger equations with quadratic interaction, Ann. Inst. H. Poincare Anal. Non Lineaire 30 (2013), no. 4, 661--690.
  • (with J. Byeon), Semi-classical standing waves for nonlinear Schr\"odinger equations at structurally stable critical points of the potential, J. Eur. Math. Soc. (JEMS) 15 (2013), no. 5, 1859 1899.
  • (with J. Byeon), Semiclassical standing waves with clustering peaks for nonlinear Schr\"odinger equations, Memoir Amer. Math. Soc. 229 (2014), no. 1076, viii+89 pp.
  • (with P. Felmer, S. Martinez), High energy rotation type solutions of the forced pendulum equation, Nonlinearity 26 (2013) 1473--1499.
  • (with J. Byeon), Nonlinear elliptic equations in strip-like domains, Advanced Nonlinear Studies 12 (2012), 749--765.
  • (with N. Ikoma), A local mountain pass type result for a system of nonlinear Schr\"odinger equations, Calc. Var. Partial Diff. Eq., 2011, Volume 40, Numbers 3--4, Pages 449--480.
  • (with J. Hirata, N. Ikoma), Nonlinear scalar field equations in $\R^N$: mountain pass and symmetric mountain pass approaches, Topol. Methods Nonlinear Anal. 35 (2010), no. 2, 253--276.
  • (with Y. Sato) Sign-changing multi-bump solutions for nonlinear Schr\"odinger equations with steep potential wells, Trans. Amer. Math. Soc. 361 (2009) 6205--6253.
  • (with P. Felmer, S. Martinez) Uniqueness of radially symmetric positive solutions for $-\Delta u+u=u^p$ in an Annulus, J. Diff. Eq. 245 (2008), 1198--1209.
  • (with J. Byeon, L. Jeanjean) Standing waves for nonlinear Schr\"odinger equations with a general nonlinearity: one and two dimensional cases, Comm. Partial Diff. Eq. 33 (2008), 1113--1136.
  • (with P. Felmer, S. Martinez) Highly oscillatory behavior of the activator in the Gierer and Meinhardt system, Math. Ann. 340 (2008), no. 4, 749--773.
  • (with C. Carminati, E. Sere) The fixed energy problem for a class of nonconvex singular Hamiltonian systems, J. Diff. Eq. 230 (2006), no. 1, 362--377.
  • (with P. Felmer, S. Martinez) On the number of positive solutions of singularly perturbed 1D NLS, J. Eur. Math. Soc. 8, Issue 2, 253-268 (2006).
  • (with P. Felmer, S. Martinez) High frequency solutions for singularly perturbed 1D nonlinear schr\"odinger equation, Arch. Rat. Mech. Anal. 182 no. 2, 333--366, 2006.
  • (with P. Felmer, S. Martinez) High frequency chaotic solutions for a slowly varying dynamical system, Ergodic Theory and Dynamical Systems, 26, no. 2, 253--268 (2006).
  • (with T. Ide, K. Kurata) Multiple Stable Patterns for Some Reaction-Diffusion Equation in Disrupted Environments, Discrete Contin. Dyn. Syst. 14 (2006), no. 1, 93--116.
  • (with P. Felmer, S. Martinez) Multi-clustered high energy solutions for a phase transition problem, Proc. Roy. Soc. Edinburgh 135A (2005), 731-765.
  • (with L. Jeanjean) A positive solution for a nonlinear Schr\"{o}dinger equation on $\R^N$, Indiana Univ. Math. J. 54 No. 2 (2005), 443-464.
  • (with S. Adachi, M. Terui) A remark on periodic solutions of singular Hamiltonian systems, NoDEA: Nonlinear Differential Equations and Applicatios, 12, No. 3, 265 - 274 (2005).
  • (with L. Jeanjean) Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities, Calculus of Variations and Partial Differential Equations Vol. 21, No. 3, 287 - 318 (2004).
  • (with L. Jeanjean) A note on a mountain pass characterization of least energy solutions, Advanced Nonlinear Studies 3 (2003), 461-471.
  • (with Y. Ding) Multiplicity of positive solutions of a nonlinear Schr\"odinger equation, Manuscripta Mathematica 112 (2003), 109-135.
  • (with L. Jeanjean) A remark on least energy solutions in R^N, Proc. Amer. Math. Soc. 131, (2003) 2399-2408
  • (with K. Nakashima) Clustering layers and boundary layers in spatially inhomogeneous phase transition problems, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire 20 (2003), 107--143.
  • (with P.Felmer, M. del Pino) An elementary method for the construction of complex solutions for nonlinear Schr\"odinger equations, Nonlinearity 15 (2002), no. 5, 1653--1671.
  • (with L. Jeanjean) A positive solution for an asymptotically linear elliptic problem on R^N autonomous at infinity, ESAIM Control Optim. Calc. Var. 7 (2002), 597--614.
  • (with S. Adachi) Existence of positive solutions for a class of nonhomogeneous elliptic equations in $\boldR^N$, Nonlinear Analysis: T.M.A. 48 (2002), 685-705.
  • (with S. Adachi) Multiple positive solutions for nonhomogeneous elliptic equations, Nonlinear Analysis: T.M.A. 47 (2001), 3783-3793
  • (with P. Felmer) Scattering solutions for planar singular hamiltonian systems via minimization, Adv. Diff. Eqn. 5 (2000), 1519-1544.
  • (with S. Adachi) Four positive solutions for the semilinear elliptic equation: $-\Delta u+u=a(x)u^p+f(x)$ in $\boldR^N$, Calculus of Variations and Partial Differential Equations, 11 (2000), 63-95.
  • (with S. Adachi) Trudinger type inequalities in $\boldR^N$ and their best exponents, Proc. Amer. Math. Soc. 128 (2000), 2051-2057.
  • (with P. Felmer) Hyperbolic-like solutions for singular Hamiltonian systems, NoDEA Nonlinear Differential Equations Appl. 7 (2000), 43-65.
  • Periodic solutions for singular Hamiltonian systems and closed geodesics on non-compact Riemannian manifolds, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire 17 (2000), 1-33.
  • Prescribed energy problem for a singular Hamiltonian system of 2-body type, Progress in nonlinear analysis (Tianjin, 1999), 359--369, Nankai Ser. Pure Appl. Math. Theoret. Phys., 6, World Sci. Publishing, River Edge, NJ, 2000.
  • (with Y. Kabeya) Uniqueness of positive radial solutions of semilinear elliptic equaitons in $\R^N$ and Sere's non-degeneracy condition, Comm. Partial Differential Equations 24 (1999), 563--598.
  • (with A. Ambrosetti) On Keplerian N-body type problems, in "Nonlinear Analysis and continuum mechanics: Paper for the 65-th birthday of James Serrin" (G. Buttazzo, G.P. Galdi, E. Lanconelli, P. Pucci ed.) Springer 1998, 15-25.
  • Multiple positive solutions for some nonlinear elliptic systems, Topological Methods in Nonlinear Analysis 10 (1997), 15-45.
  • Periodic solutions of first order singular Hamiltonian systems, Nonlinear Anal. 26 (1996), 791-706.
  • (with F. Giannoni, L. Jeanjean) Homoclinic orbits on non-compact Riemannian manifolds for second order Hamiltonian systems, Rend. Sem. Mat. Univ. Padova 93 (1995), 153-176.
  • (with Y. Sasahara) A remark on positive radial solutions of the elliptic equation $\Delta u+K(\vert x\vert )u\sp {(n+2)/(n-2)}=0$ in ${\bf R}\sp n$, Proc. Amer. Math. Soc. 123 (1995), 527--531.
  • A prescribed-energy problem for a conservative singular Hamiltonian system, Arch. Rational Mech. Anal. 128 (1994), 127-164.
  • (with A. Ambrosetti, E. Vitillaro, Enzo) Periodic solutions with prescribed energy for some Keplerian $N$-body problems, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire 11 (1994), 613-632.
  • A note on generalized solutions of singular Hamiltonian systems, Proc. Amer. Math. Soc. 122 (1994), 275-284.
  • A note on the existence of multiple homoclinic orbits for a perturbed radial potential, NoDEA Nonlinear Differential Equations Appl. 1 (1994), 149-162.
  • A prescribed energy problem for a singular Hamiltonian system with a weak force, J. Funct. Anal. 113 (1993), 351-390.
  • Noncollision solutions for a second order singular Hamiltonian system with weak force, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire 10 (1993), 215-238.
  • Non-collision solutions of singular Hamiltonian systems, in "Nonlinear PDE-JAPAN symposium 2, 1991 (Kyoto, 1991)", 229-248, Kinokuniya, Tokyo, 1993.
  • Multiple periodic solutions of a superlinear forced wave equation, Ann. Mat. Pura Appl. (4) 162 (1992), 43-76.
  • Homoclinic orbits in a first order superquadratic Hamiltonian system: convergence of subharmonic orbits, J. Differential Equations 94 (1991), 315-339.
  • (with P.H. Rabinowitz) Some results on connecting orbits for a class of Hamiltonian systems, Math. Z. 206 (1991), 473-499.
  • Homoclinic orbits for a singular second order Hamiltonian system, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire 7 (1990), 427-438.
  • (with R. Kajikiya) Existence of infinitely many solutions for some superlinear elliptic equations, J. Math. Anal. Appl. 149 (1990), 313-321.
  • Morse indices at critical points related to the symmetric mountain pass theorem and applications, Comm. Partial Differential Equations 14 (1989), 99-128.
  • Infinitely many periodic solutions for the equation: $u\sb {tt}-u\sb {xx}\pm \vert u\vert \sp {p-1}u=f(x,t)$. II, Trans. Amer. Math. Soc. 307 (1988), 615-645.
  • Forced vibrations for a superlinear vibrating string equation, in "Recent topics in nonlinear PDE, III (Tokyo, 1986)", 247-266, North-Holland, Amsterdam, 1987.
  • Infinitely many periodic solutions for a superlinear forced wave equation, Nonlinear Anal. 11 (1987), 85--104 and Proc. Japan Acad. Ser. A Math. Sci. 61 (1985), 341-344.
  • Density of the range of a wave operator with nonmonotone superlinear nonlinearity, Proc. Japan Acad. Ser. A Math. Sci. 62 (1986), 129-132.
  • Infinitely many periodic solutions for the equation: $u\sb {tt}-u\sb {xx}\pm \vert u\vert \sp {s-1}u=f(x,t)$, Comm. Partial Differential Equations 10 (1985), 1317-1345 and Proc. Japan Acad. Ser. A Math. Sci. 61 (1985), 70-73.
  • On the range of wave operators, Tokyo J. Math. 8 (1985), 377-387.