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Professor of Mathematics – Departament of Mathematics – University of Brasília – UnB .

** Associate Professor III in Mathematics and Director of the Institute of Exact Sciences – University of Brasília




Research

I'm interested in Partial Differential Equations, Ellipitc Problems, Schrödinger Equations, Variational Methods and Ergodic Theory.





Published Papers

1) The double transpose of the Ruelle operator
with VAN ENTER, A. C. D. and CIOLETTI, L. M.
Monatshefte Fur Mathematik, p. 01-22, 2023.

2) Kirchhoff-Boussinesq type problems with positive and zero mass
with CARLOS, R. D. and FIGUEIREDO, G. J. M.
APPLICABLE ANALYSIS, 2023.

3) Existence and nonexistence of solutions to nonlocal elliptic problems
with BUENO, H.; PEREIRA, G. A. and SILVA, E. D.
Partial Differential Equations and Applications, v. 3, n. 8, 2022.

4) Generalized quasilinear equations with critical growth and nonlinear boundary condition (for the special issue honoring the memory of late Professor Lazer)
with MAIA, L. A. and OLIVEIRA JUNIOR, J. C.
Electronic Journal of Differential Equations, v. 1, p. 327-344, 2022.

5) On the dimension of the space of harmonic functions on transitive shift spaces
with CIOLETTI, L. M.; MELO, L. and SILVA, E. A.
Advances in Mathematics, v. 385, 107758, 2021.

6) Existence of least energy positive and nodal solutions for a quasilinear Schrödinger problem with potentials vanishing at infinity
with FIGUEIREDO, G. J. M. and MOREIRA NETO, S. I.
Journal of Mathematical Physics, v. 62, p. 091501, 2021.

7) Mini-max algorithm via Pohozaev manifold
with RAOM, D.; MAIA, L. A. and SOBRAL, Y.
Nonlinearity, v. 34, p. 642-668, 2021.

8) Multiplicity and regularity results for a class of quasilinear Schrödinger equations involving a nonlinearity concave at the origin
with MOURA, E. L.; OLIVEIRA JUNIOR, J. C. and FIGUEIREDO, G. J. M.
Mediterranean Journal of Mathematics, v. 18, 139, 2021.

9) Nonlinear perturbations of a periodic fractional Laplacian with supercritical growth
with FIGUEIREDO, G. J. M. and MOREIRA NETO, S. I.
Topological Methods in Nonlinear Analysis, v.58, p. 335-349, 2021.

10) Quasilinear Equations Involving Critical Exponent and Concave Nonlinearity at the Origin
with FIGUEIREDO, G. J. M. and Oliveira Junior, J. C.
Milan Journal of Mathematics, 2020.

11) Non-cooperative elliptic systems modeling interactions of Bose-Einstein condensates in R^N
with MAIA, L. A. and COSTA, M. S. S.
Zeitschrift Fur Angewandte Mathematik Und Physik, 2020.

12) Nodal solution for a planar problem with fast increasing weights
with FIGUEIREDO, G. J. M. and FURTADO, M. F.
Topological Methods in Nonlinear Analysis, p. 1-19, 2019.

13) Bound state for a strongly coupled nonlinear Schrödinger system with saturation
with MAIA, L. A. and MOURA, E. L.
Milan Journal of Mathematics (Printed ed.), p. 1-29, 2019.

14) A Variational Principle for the Specific Entropy for Symbolic Systems with Uncountable Alphabets
with Aguiar, D. and Cioletti, L.
Mathematische Nachrichten - Online First, 2018.

15) Quasilinear asymptotically linear Schrödinger problem in R^N without monotonicity
with MIYAGAKI, O. H. and MOREIRA NETO, S. I.
Electronic Journal of Differential Equations. Vol. 2018, No. 164, p. 1-21, 2018.

16) Positive ground state solutions for quasicritical the fractional Klein–Gordon–Maxwell system with potential vanishing at infinity
with MIYAGAKI, O. H. and MOURA, E. L.
Complex Variables and Elliptic Equations (Print), p. 1-15, 2018.

17) A non periodic and asymptotically linear indefinite variational problem in R^N
with MAIA, L. A. and OLIVEIRA JUNIOR, J. C.
Indiana Univ. Math. J. 66 No. 1, p. 31–54, 2017.

18) Semilinear elliptic problems with combined nonlinearities on the boundary
with FURTADO, M. F. and SILVA, E. D.
Annali di Matematica Pura ed Applicata, p. 1–15, 2017.

19) The first eigenvalue for a quasilinear Schrödinger operator and its application
with MIYAGAKI, O. H. and MOREIRA NETO, S. I.
Applicable Analysis, p. 1-14, 2017.

20) Positive ground state solutions for quasicritical Klein-Gordon-Maxwell type systems with potential vanishing at infinity
with MIYAGAKI, O. H. and MOURA, E. L.
Electronic Journal of Differential Equations. Vol. 2017, No. 154, p. 1-11, 2017.

21) A quasi-linear Schrödinger equation with indefinite potential
with MAIA, L. A. and OLIVEIRA JUNIOR, J. C.
Complex Variables and Elliptic Equations (Print), p. 1-13, 2016.

22) Existence of solutions for a nonperiodic semilinear Schrödinger equation
with DE MARCHI, R.
Complex Variables and Elliptic Equations (Print), p. 1-13, 2016.

23) Nonautonomous and non periodic Schrödinger equation with indefinite linear part
with MAIA, L. A. and OLIVEIRA JUNIOR, J. C.
Journal of Fixed Point Theory and Applications, p. 1-20, 2016.

24) Positive and Nodal Solutions of Nonlinear Schrodinger Equations in a Saturable Medium
with MAIA, L. A.
Advanced Nonlinear Studies, v. 15, p. 191-219, 2015.

25) Two solutions for an elliptic equation with fast increasing weight and concave-convex nonlinearities
with FURTADO, M. F. and da SILVA, J. P. P.
Journal of Mathematical Analysis and its Applications (Print), v. 416, p. 698-709, 2014.

26) Bound states of a nonhomogeneous nonlinear Schrödinger equation with non symmetric potential
with MAIA, L. A. and LEHRER, R.
NoDEA. Nonlinear Differential Equations and Applications (Printed ed.), p. 651-672, 2014.

27) Multiple solutions for a semilinear problem with combined terms and nonlinear boundary conditions
with FURTADO, M. F.
Nonlinear Analysis, v. 74, p. 4820-4830, 2011.

28) Sign-changing Solutions for a Schrödinger Equation with Saturable Nonlinearity
with MAIA, L. A.
Milan Journal of Mathematics (Printed ed.), v. 79, p. 259-271, 2011.





Teaching

"The enchanting charms of this sublime science, mathematics, reveal only to those who have the courage to go deeply into it." Carl Friedrich Gauss


Analysis I; Calculus I; Calculus II; Topics in Mathematics; Seminary on Nonlinear Functional Analysis; Research Internship in Analysis; Educational Evaluation





Orientations Completed

"To be a teacher in the right sense is to be a learner. I am not a teacher, only a fellow student." Soren Kierkegaard


1) Maristela Barbosa Cardoso - Doctorate in Science - 2024 - Ricardo Ruviaro (Advisor)
Nonautonomous and non periodic Schrödinger equation with asymptotic growth in R^N.

2) Gilberto da Silva Pina - Doctorate in Science - 2022 - Ricardo Ruviaro (Co-advisor)
A natural constraint for solving Schrödinger equations with G-symmetry and general nonlinerities.

3) Carolina Santos de Almeida - Profmat - 2022 - Ricardo Ruviaro (Advisor)
Alcances da Matemática via olimpíadas e projetos de Iniciação Científica: Uma abordagem social e experimental.

4) Paulo Cesar Bernardo Silva - Profmat - 2020 - Ricardo Ruviaro (Advisor)
Uma estratégica para a OBMEP: o impacto das demonstrações sob a perspectiva da aprendizagem singnificativa.

5) Lorranny Cruz Santos - Profmat - 2019 - Ricardo Ruviaro (Advisor)
Uma abordagem histórica, demonstrativa e investigativa de tópicos em Matemática no Ensino Básico.

6) Fausto Fernandes da Silva Camelo - Profmat - 2018 - Ricardo Ruviaro (Advisor)
Um critério de divisibilidade universal sob a ótica da teoria de aprendizagem significativa de Ausubel.

7) Antonio Dantas Costa Neto - Profmat - 2017 - Ricardo Ruviaro (Advisor)
O Ensino e a Aprendizagem de Cálculo 1 na Universidade: Entender e Intervir.

8) Mayra Soares da Silva Costa - Master Science - 2016 - Ricardo Ruviaro (Advisor)
Um problema elíptico no R^N assintoticamente linear e autonomo no infinito

9) Wesley de Freitas Mendes - Master Science - 2016 - Ricardo Ruviaro (Advisor)
Uma classe de problemas elípticos assintoticamente linear em R^N.

10) Paulo Luiz da Silva Ramos - Profmat - 2016 - Ricardo Ruviaro (Advisor)
Razão Áurea: Uma a aplicação para o ensino médio.

11) Maryna de Oliveira Paiva - Profmat - 2015 - Ricardo Ruviaro (Advisor)
Aplicações do Estudo da Derivada no Nível Básico de Ensino Associado à Resolução de Questões de Máximos e Mínimos.

12) Evelyn Gabrielle Monteiro Gomes da Silva - Profmat - 2015 - Ricardo Ruviaro (Advisor)
Contextualização histórica para o estudo da trigonometria e construção do teodolito no Ensino Fundamental.

13) Marco Antônio Alves Dias - Profmat - 2015 - Ricardo Ruviaro (Advisor)
Aplicações do Estudo do Cálculo Integral no Nível Básico de Ensino Associado à Resolução do Cálculo de Áreas de Figuras Planas.

14) Bertha Katherine Rodríguez Chávez - Master Science - 2015 - Ricardo Ruviaro (Advisor)
Efeitos combinados de não-linearidades côncavas e convexas em alguns problemas elípticos.

15) Marcio Lopes Campolino - Profmat - 2014 - Ricardo Ruviaro (Advisor)
Translação e Rotação de Cônicas em R^2.

16) Leonardo Miranda de Castro - Profmat - 2014 - Ricardo Ruviaro (Advisor)
O Cálculo Variacional e as Curvas Cicloidais.

17) Adriana Hartmann - Profmat - 2014 - Ricardo Ruviaro (Advisor)
O Desporto Orientação como Ferramenta para o Ensino da Matemática.
This Master's dissertation originate the paper





Curriculum

Curriculum Lattes





Refereeing for Journals

  • Journal of Mathematical Physics
  • Zeitschrift für angewandte Mathematik und Physik
  • Dynamics of Partial Differential Equations
  • Discrete and Continuous Dynamical Systems
  • Electronic Journal of Differential Equation
  • Complex Variables and Elliptic Equations
  • NEXUS Mathematicæ
  • Ciência e Natura




Others

PhD thesis - Mathematics Departament of the University of Brasília:
Existência de soluções positivas ou nodais para problemas assintoticamente lineares

Master Science Dissertation - Mathematics Departament of the University of Brasília:
Teorema de Bernstein

Contact

Departamento de Matemática - Universidade de Brasília
Campus Universitário Darcy Ribeiro
ICC Centro - Bloco A - Asa Norte
70910-900 Brasília - DF
Brasil
Phone:+55 61 3107-6399
e-mail: ruviaro@unb.br and ruviaro@mat.unb.br
ORCID: 0000-0002-3255-2446