Korean J. Math.  Vol 26, No 1 (2018)  pp.9-21
DOI: https://doi.org/10.11568/kjm.2018.26.1.9

Elliptic boundary value problem with two singularities

Tacksun Jung, Q-Heung Choi


We investigate existence and multiplicity of the solutions for elliptic boundary value problem with two singularities. We obtain one theorem which shows that there exists at least one nontrivial weak solution under some conditions on which the corresponding functional of the problem satisfies the Palais-Smale condition. We obtain this result by variational method and critical point theory.


Elliptic boundary value problem; Singular potential; variational reduction method

Subject classification

35J50, 35J55


Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education,Science and Technownology (2017R1D1A1B03030024) and by the Ministry of Science, ICT and Future Planning (NRF-2017R1A2B4005883).

Full Text:



C. O. Alves, D. C. De Morais Filho, and M. A. Souto, On systems of equations involving subcritical or critical Sobolev exponents, Nonlinear Analysis, Theory, Meth. and Appl. 42 (2000), 771–787. (Google Scholar)

A. Ambrosetti and G. Prodi, On the inversion of some differential mappings with singularities between Banach spaces, Ann. Mat. Pura. Appl. 93 (1972), 231–246. (Google Scholar)

K. C. Chang, Ambrosetti-Prodi type results in elliptic systems, Nonlinear Analysis TMA. 51 (2002), 553–566. (Google Scholar)

D. G. de Figueiredo, Lectures on boundary value problems of the Ambrosetti-Prodi type, 12 Seminario Brasileiro de An ́alise, 232-292 (October 1980). (Google Scholar)

M. Ghergu and V. D. Raˇdulescu, Singular elliptic problems Bifurcation and Asymptotic Analysis, Clarendon Press Oxford 2008. (Google Scholar)

Rabinowitz, P. H., Minimax methods in critical point theory with applications to differential equations, CBMS. Regional conf. Ser. Math. 65, Amer. Math. Soc., Providence, Rhode Island (1986). (Google Scholar)


  • There are currently no refbacks.

ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr