A Probabilistic Approach for Nonlinear Equations Involving the Fractional Laplacian and a Singular Operator
✍ Scribed by Benjamin Jourdain; Sylvie Méléard; Wojbor A. Woyczynski
- Publisher
- Springer Netherlands
- Year
- 2005
- Tongue
- English
- Weight
- 366 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0926-2601
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📜 SIMILAR VOLUMES
that D is an unbounded domain in R2 with a compact boundary aD and k(z) is a strictly positive Holder continuous function on D such that .I (log (11~11))" k(r) dr < 00, IIZll>Q for some constant a > 0. In this paper, we study the nonlinear elliptic equation (1/2)A~ = Ic(x)u"(z) on D, where o E (1,2]
The existence and multiplicity of weak solutions is established for a class of concave-convex elliptic systems of the form: R 2 \ {(0, 0)}, the weight m(x) is a positive bounded function and a(x), b(x) ∈ C (Ω) are functions which change sign in Ω. Our technical approach is based on the Nehari manifo