Elliptic equations and systems with several kinds of interaction with the spectrum

• Grant number: 14/25398-0
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2015
• End date: August 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Eugenio Tommaso Massa
• Grantee: Eugenio Tommaso Massa
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• City of the host institution: São Carlos

Abstract

It is largely known that the solvability of a semilinear elliptic problem depends strongly on the interaction of the nonlinearity with the spectrum of the operator. In this project we propose several lines of research that aim at establishing existence and multiplicity of solutions for semilinear and quaselinear elliptic problems, including systems, where the nonlinearity exhibits different behaviors with respect to the spectrum of the operator.Some of the proposed researches are new, while others are a continuation of previous works by the proponent and his collaborators. (AU)

Scientific publications

(9)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

CALANCHI, MARTA; MASSA, EUGENIO; RUF, BERNHARD. WEIGHTED TRUDINGER-MOSER INEQUALITIES AND ASSOCIATED LIOUVILLE TYPE EQUATIONS. Proceedings of the American Mathematical Society, v. 146, n. 12, p. 5243-5256, DEC 2018. (14/25398-0)

MASSA, EUGENIO; ROSSATO, RAFAEL ANTONIO. THREE SOLUTIONS FOR AN ELLIPTIC SYSTEM NEAR RESONANCE WITH THE PRINCIPAL EIGENVALUE. DIFFERENTIAL AND INTEGRAL EQUATIONS, v. 30, n. 3-4, p. 207-230, MAR-APR 2017. (10/06411-4, 14/25398-0)

MASSA, EUGENIO; PERON, ANA PAULA; PORCU, EMILIO. Positive Definite Functions on Complex Spheres and their Walks through Dimensions. Symmetry Integrability and Geometry-Methods and Applications, v. 13, 2017. (14/25398-0, 14/25796-5, 16/03015-7)

ITURRIAGA, LEONELO; LORCA, SEBASTIAN; MASSA, EUGENIO. MULTIPLE POSITIVE SOLUTIONS FOR THE M-LAPLACIAN AND A NONLINEARITY WITH MANY ZEROS. DIFFERENTIAL AND INTEGRAL EQUATIONS, v. 30, n. 1-2, p. 145-159, JAN-FEB 2017. (14/25398-0)

MASSA, E.; PERON, A. P.; PIANTELLA, A. C.. Estimates on the derivatives and analyticity of positive definite functions on R-m. ANALYSIS MATHEMATICA, v. 43, n. 1, p. 89-98, MAR 2017. (14/25796-5, 14/25398-0)

ITURRIAGA, LEONELO; MASSA, EUGENIO. EXISTENCE, NONEXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS FOR THE POLY-LAPLACIAN AND NONLINEARITIES WITH ZEROS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 38, n. 8, p. 3831-3850, AUG 2018. (14/25398-0)

ITURRIAGA, LEONELO; MASSA, EUGENIO. Sobolev versus Holder local minimizers in degenerate Kirchhoff type problems. Journal of Differential Equations, v. 269, n. 5, p. 4381-4405, AUG 15 2020. (19/19699-0, 14/25398-0)

CASTRO, MARIO H.; MASSA, EUGENIO; PERON, ANA PAULA. Characterization of Strict Positive Definiteness on products of complex spheres. POSITIVITY, v. 23, n. 4, p. 853-874, SEP 2019. (16/03015-7, 14/25796-5, 14/25398-0, 16/09906-0)

ITURRIAGA, LEONELO; MASSA, EUGENIO. On necessary conditions for the comparison principle and the sub- and supersolution method for the stationary Kirchhoff equation. Journal of Mathematical Physics, v. 59, n. 1, JAN 2018. (14/25398-0)