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Two nontrivial solutions of a class of elliptic equations with singular term (with J. Chen, K. Murillo), Dynamical Systems and Differential Equations, DCDS Supplement 2011. Proceedings of the 8th AIMS International Conference, Wei Feng et al., 272-281, Dresden (Germany), 2011. ISBN: 978-1-60133-007-9


ABSTRACT: We consider the existence of nontrivial solutions of the equation

    \[-\Delta u -{\frac{\lambda }{{|x|^{2}}}}u= |u|^{2^{\ast}-2}u  + \mu|x|^{\alpha-2}u + f(x)|u|^{\gamma},\quad x\in \Omega\backslash\{0\},\:\:\: u\in H^1_0(\Omega),\]

where 0\in\Omega is a smooth bounded domain in \mathbb{R}^N (N\geq 3). By variational methods and Nehari set techniques, we show that this equation has at least two nontrivial solutions in H^1_0(\Omega), under some additional hypotheses on \lambda>0, \mu>0, \alpha>0, 0\leq\gamma<1 and f\in L^\infty(\Omega), which may be sign-changing. If f>0 then the solutions are positive.


Download: Preprint version (RIA |  download) / Publisher version (Discrete Contin. Dyn. Syst.)
Extra info: (P100/2011-09) (free/open access)

REF. DATE: 22 September 2011 CREATED/MODIFIED: 14 January 2016 VIEW POST 177 views No Comment

Existence and multiplicity of solutions for the noncoercive Neumann p-Laplacian (with N.S. Papageorgiou), Electronic Journal of Differential Equations, Conference 18 (2010), pp. 57-66,
(special issue of the Conference “Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems 2007”, in 2009).
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REF. DATE: 9 March 2010 CREATED/MODIFIED: 19 January 2012 VIEW POST 234 views No Comment

Exact and approximate solutions of reaction-diffusion-convection equations (with M.M. Rodrigues), AIP-Proceedings of International Conference on Boundary Value Problems-BVP 2008, A. Cabada, E. Liz, J.J. Nieto, 10 pp, Santiago de Compostela, 2009.
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REF. DATE: 9 September 2009 CREATED/MODIFIED: 19 January 2012 VIEW POST 301 views No Comment

Stability analysis of Raman propagation equations (with B. Neto, M.M. Rodrigues, P.S. Andre), IEEE – Conference Proceedings, 11th International Conference Transparent Optical Networks, 2009 – ICTON ’09 (IEEE – Conference Proceedings), 1-4, Ponta Delgada – Açores, 2009.
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REF. DATE: 21 January 2009 CREATED/MODIFIED: 14 January 2016 VIEW POST 358 views No Comment

Stability analysis of Raman propagation equations of three and higher dimensions (with B. Neto, M.M. Rodrigues, R.M. Morais, A.N. Pinto, P.S. Andre), Optical Networks – SEON, 2008.
(myid-76)

REF. DATE: 21 September 2008 CREATED/MODIFIED: 14 January 2016 VIEW POST 270 views No Comment

Interactive, collaborative and adaptative learning tools (with A. Breda, M.M. Rodrigues), in: Proceedings of the 4th International Conference on Web Information Systems and Technology, INSTICC, José Cordeiro et al. (eds), 456-459, Funchal-Madeira, 2008.
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REF. DATE: 8 September 2008 CREATED/MODIFIED: 19 January 2012 VIEW POST 216 views No Comment

TexMat – a multimedia constructivist learning environment (with A. Breda, J. Martins), in: Proceedings of the 11th Asian Technology Conference in Mathematics (ATCM), Sung-Chi Chu et al. (eds), 12-16, Hong Kong, 2006.
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REF. DATE: 8 September 2006 CREATED/MODIFIED: 19 January 2012 VIEW POST 256 views No Comment

BioMat – a multi-mode educational game (with A. Breda), in: Proceedings of ED-MEDIA’2005, 1359-1366, Canada, 2005.
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REF. DATE: 8 September 2005 CREATED/MODIFIED: 19 January 2012 VIEW POST 204 views No Comment

An application of control-theoretic methods to digital arithmetic algorithms (with A. Sarychev, A. Pereira, R. Rodrigues), in: Proceedings of the 10th Mediterranean Conference on Control and Automation, Lisbon, Portugal, 2002.
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REF. DATE: 8 September 2002 CREATED/MODIFIED: 19 January 2012 VIEW POST 191 views No Comment

Coordinates of first kind and periodic time-variant feedback stabilization, in: Proceedings of the FJEM – Control Theory and Stabilization, Dijon, France, 2002.
(myid-18)

REF. DATE: 8 September 2002 CREATED/MODIFIED: 18 January 2012 VIEW POST 173 views No Comment

Time-variant feedback stabilization of a system of two rolling bodies (with A. Sarychev), in: Proceedings of the 5th Portuguese Conference on Automatic Control, Aveiro, Portugal, 2002.
(myid-16)

REF. DATE: 8 September 2002 CREATED/MODIFIED: 19 January 2012 VIEW POST 265 views No Comment

Quantitative assessment of retinal structures and lesions (with H. Araújo, J. Cunha-Vaz, L. Ribeiro, D. Torres), in: Proceedings of RecPad95, 6.5.1-6.5.6, Aveiro, Portugal, 1995.
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REF. DATE: 8 September 1995 CREATED/MODIFIED: 14 January 2016 VIEW POST 187 views No Comment