Abstract
We prove the existence of infinitely many solutions for the nonlinear elliptic equation Δu+f(.,u)=0 in D with u>0 in D and u=0 on ∂D, where D={x∈R 2:|x|>1} and f is a measurable function dominated by a regular function q such that q(x,Log|x|) is in a some Kato class.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chung, K. L and Zhao, Z.: From Brownian Motion to Schrödinger's Equation, Springer, Berlin, 1995.
Selmi, M.: 'Inequalities for Green functions in a Dini-Jordan domain in ℝ2', Potential Anal. 13 (2000), 81-102.
Zhang, QiS. and Zhao, Z.: 'Singular solutions of semilinear elliptic and prabolic equations', Math. Ann. 310 (1998), 777-794.
Zhao, Z.: 'On the existence of positive solutions of nonlinear elliptic equations-a probabilistic potential theory approach', Duke Math. J. 69 (1993), 247-258.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Maatoug, L. Positive Solutions of a Nonlinear Elliptic Equation in {x∈R2:|x|>1}. Potential Analysis 16, 193–203 (2002). https://doi.org/10.1023/A:1012684223602
Issue Date:
DOI: https://doi.org/10.1023/A:1012684223602