Infinitely many positive solutions for an elliptic problem with critical or supercritical growth

By Jun-cheng Wei, Shusen Yan. 2011

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Abstract We prove that for some supercritical exponents p > N + 2 N − 2 and for some smooth domains D in R N there are infinitely many (distinct) positive solutions to the following Lane–Emden–Fowler equation: { − Δ u = u p , u > 0 , in D , u = 0 , on ∂ D This seems to be the first result for such type of equations.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/970d399d9a99db576d7f1e516474bf1e3b9c5cfb