## Publications

# Refereed Articles (last 20 years)

- (2023) On Heterogeneous Radially Symmetric Semilinear Elliptic Equations with Critical Nonlinearities in R^2, Nonlinear Analysis – Real World Applications,
**p. 103-118**(with H. Tehrani). - (2022) Multiplicity Results for Semilinear Heterogeneous Problems in Exterior Domains of R^2 involving Subcritical or Critical Nonlinearities ‘a la Trudinger-Moser, J. Math. Anal. Appl.
**510**, p. 125-145 (with H. Tehrani). - (2021) The Nehari Manifold for Indefinite Kirdhhoff Problem with Caffarelli-Kohn-Nirenberg Type Critical Growth, Topological Methods in Nonlinear Analysis
**58**, p. 105-134 (with J.M do O’ and P.K. Mishra). - (2019) A Note on Breaking of Symmetry for a Class of Variational Problems, Appl. Math. Letters
**98**, p. 329-335 (with Z. Fang). - (2019) Existence of Solution for a Class of Quasilinear Schrodinger Equation in R^N with Zero-Mass, J. Math. Anal. Appl.
**477**, p. 912-929 (with C. Alves and O. Miyagaki). - (2018) Extremal Solutions of Logistic-Type Equations in Exterior Domains in R^2, Nonlinear Anal.
**276**, p. 272-287 (with S. Carl and H. Tehrani). - (2018) Existence and Concentration of Positive Solutions for Nonlinear Kirchhoff-Type Problems with General Critical Nonlinearity, Proc. Edinb. Math. Soc.
**61**, p. 1023-1040 (with J. do O’ and J.J. Zhang). - (2017) Existence of Nonnegative Solution for a p-Laplacian Semipositone Problem with Nonlinear Boundary Conditions, I. J. Math. Anal.
**11**, p. 921-931 (with A. Drame and D.A. Bardac-Vlada). - (2017) D^{1,2}(R^N) versus C(R^N) Local Minimizer on Manifolds and Multiple Solutions for Zero-Mass Equations in R^N, Adv. Calc. Var.
**11**, p. 257-272 (with S. Carl and H. Tehrani). - (2017) Fractional Sobolev Space of Symmetric Functions and Hamiltonian Elliptic System of the Henon Type, (with D.G. Figueiredo, E.M. dos Santos, and O.H. Miyagaki).
- (2017) Multiple Positive Solutions for a Class of Variational Systems, Topol. Methods Nonlinear Anal.
**50**, p. 1-8 (with A. Castro and R. Shivaji). - (2016) A Variational Approach to Superlinear Semipositone Elliptic Problems, Proc. Amer. Math. Soc.
**145**, p. 2661-2675 (with H. Quoirin and H. Tehrani). - (2016) Semiclassical States of p-Laplacian Equations with a General Nonlinearity in Critical Case, J. Math. Phys.
**7**, 12 pp (with J. do O’ and J.J. Zhang). - (2016) D^{1,2}(R^N) versus C(R^N) Local Minimizer and Hopf-Type Maximum Principle, J. Differential Equations
**261**, p. 2006-2025 (with S. Carl and H. Tehrani). - (2015) Extremal and Sign-Changing Solutions of Supercritical Logistic-Type Equations in R^N, Calc. Var.
**54**, p. 4143-4164 (with S. Carl and H. Tehrani). - (2015) Asymptotics and Ground States for Fractional Henon Systems, Progress in Nonlinear Differential Equations and Their Applications (with O.H. Miyagaki, M. Squassina, and J. Yang), Alexandre Nolasco de Carvalho et al, (eds.), DOI 10.1007/978-3-319-19902-3_10@ Springer International Publishing Switzerland 2015.
- (2014) Concentration Profiles for the Trudinger -Moser Functional are Shaped Like Toy Pyramids, J. Functional Analysis
**266**, p. 676-692 (with K. Tintarev). - (2014) On a Class of Singular Second-Order Hamiltonian Systems with Infinitely Many Homoclinic Solutions, J. Math. Anal. Appl.
**412**, p. 200-211 (with H. Tehrani). - (2013) Existence Results for a Class of Biharmonic Equations with Critical Growth and Singular Potential in R^N, Appl. Math. Letters
**9**, p. 7-12 (with G. Zhang). - (2012) On Positive Solutions of One-Dimensional Semipositone Equations with Nonlinear Boundary Conditions, Appl. Math. Letters, Appl. Math. Letters
**25**, p. 2411-2416 (with A. Drame). - (2012) Compactness Properties of Critical Nonlinearities and Nonlinear Equations, Proc. Edinb. Math. Soc. (Series 2)
**56**, p. 427-441 (with J. do O’ and K. Tintarev). - (2012)
*Estimates at Infinity for Positive Solutions to a Class of p-Laplacian Problems in R^N*, J. Math. Anal. Appl.**391**, p. 170-182 (with H. Tehrani and R. Thomas). - (2011)
*Homoclinic Type Solutions for a Class of Differential Equations with Periodic Coefficients*, Contemporary Mathematics – AMS**540**, p. 65-78 (with C. Li). - (2010)
*Xylem Anisotropy and Water Transport – A Model for the Double Sawcut Experiment*, J. Tree Physiology**30**, p. 901-913 (with P. Schulte). - (2010)
*On Best Constants for Limiting Embeddings of Fractional Sobolev Spaces*, Advanced Nonlinear Studies**10**, p. 501-510 (with D. de Figueiredo and J. Yang). - (2010)
*Schrodinger Equations with Critical Nonlinearity, Singular Potential and a Ground State*, J. Diff. Eqs.**249**, p. 240-252 (with J. do O’ and K. Tintarev). - (2010)
*On Existence of Positive Solutions for a Class of Caffarelli-Kohn- Nirenberg Type Equations*, Colloq. Math.**120**, p. 43-62 (with J. Chabrowski). - (2009) D.G. Costa,
*On Hardy-Rellich Inequalities in R^n\{0}*, Appl. Math. Letters**22,**902-905. - (2009)
*Sharp Weighted-Norm Inequalities for Functions with Compact Support in R^n\{0}*, J. Diff. Eqs.**246,**164-182 (with F. Catrina). - (2008)
*Positive Solutions to Semilinear Elliptic Equations with Logistic-Type Nonlinearities and Constant Yield Harvesting in R^n*, Comm. Partial Diff. Eqs.**33,**1597-1610 (with P. Drabek and H. Tehrani). - (2008)
*On a Class of Schrodinger Type Equations with Indefinite Weight Functions*, Comm. Partial Diff. Eqs.**33,**1368-1394 (with J. Chabrowski). - (2008)
*A New Result on Existence of Positive Solution for Semipositone Systems*, Elect. J. Diff. Eqs.**12****,**1-11 (with A. Drame). - (2008)
*Some New and Short Proofs for a Class of Caffarelli-Kohn-Nirenberg Type Inequalities*, J. Math. Anal. Appl.**337,**311-317. - (2006)
*Simple Existence Proofs for One-Dimensional Semipositone Problems*, Proc. Royal Soc. Eddinb.**136A**, 473-493 (with H. Tehrani). - (2006)
*On a Variational Approach to Existence and Multiplicity Results for Semipositone Problems*, Elect. J. Diff. Eqs.**11**, 1-10 (with H. Tehrani and J. Yang). - (2005)
*On a Class of Critical Elliptic Equations of Caffarelli-Kohn-Nirenberg Type*, Progress Nonl. Diff. Eqs. Appl.**66**, 207-220 (with O. Miyagaki). - (2005)
*Multiplicity Results for a Class of Superlinear Elliptic Problems*, Proc. Amer. Math. Soc.**133**(with Z.-Q. Wang). - (2004)
*Nonzero Solutions for a Schrodinger Equation with Indefinite Linear and Nonlinear Terms*, Proc. Royal Soc. Edinburgh**134A**, 249-258 (with M. Ramos and H. Tehrani). - (2004)
*Unbounded Perturbations of Resonant Schrodinger Equations*, Contemporary Mathematics**357**, 101-110 (with H. Tehrani). - (2003)
*Existence and Multiplicity Results for a Class of Schrodinger Equations with Indefinite Nonlinearities*, Advances in Diff. Eqns.**8**, 1319-1340 (with H. Tehrani). - (2003)
*The Jumping Nonlinearity Problem Revisited: An Abstract Approach*, Top. Meth. in Nonl. Anal.**21**, 249-272 (with H. Tehrani). - (2003)
*Existence and Nonexistence of Least Energy Solutions of a Neumann Problem for a Semilinear Equation with Critical Sobolev Exponent and a Critical Lower-Order Perturbation*, J. Diff. Eqs.**188**, 164-202 (with P. Girao). - (2003)
*Variational Problems which are Nonquadratic at Infinity*, Proceedings of the Seminar on Morse Theory, Minimax Theory and Applications to Nonlinear Differential Equations, International Press -AMS, 39-56.

# Books and Monographs (last 20 years)

*An Invitation to Mathematical Biology was*accepted for publication in 2022 and is planned to appear after May 31, 2023.*An Invitation to Variational Methods in Differential Equations*, Birkhauser, Boston, 2007.*A First Encounter with Variational Methods in Differential Equations*, Cubo Matematica Educacional**4**(1), 251-281, 2002.*Multiplicity of Solutions in Differential Equations*, Textos de Matematica**16**, 137-154, 2002.