Geodesic
Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity
Journal of the European Mathematical Society, Tome 8 (2006) no. 2, pp. 269-288

Voir la notice de l'article provenant de la source EMS Press

In this paper we study the existence, nonexistence and multiplicity of positive solutions for the family of problems −Δu=fλ​(x,u), u∈H01​(Ω), where Ω is a bounded domain in RN, N≥3 and λ>0 is a parameter. The results include the well-known nonlinearities of the Ambrosetti–Brezis–Cerami type in a more general form, namely λa(x)uq+b(x)up , where 0≤q1≤2∗−1. The coefficient a(x) is assumed nonnegative but b(x) is allowed to change sign, even in the critical case. The notions of local superlinearity and local sublinearity introduced in [9] are essential in this more general framework. The techniques used in the proofs are lower and upper solutions and variational methods.
DOI : 10.4171/jems/52
Classification : 35-XX, 58-XX, 00-XX
Keywords: Multiplicity, semilinear elliptic problem, local sub and superlinear nonlinearities, concave-convex nonlinearities, critical exponent, upper and lower solutions, variational method 
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     title = {Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity},
     journal = {Journal of the European Mathematical Society},
     pages = {269--288},
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     volume = {8},
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Djairo Guedes de Figueiredo; Jean-Pierre Gossez; Pedro Ubilla. Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity. Journal of the European Mathematical Society, Tome 8 (2006) no. 2, pp. 269-288. doi: 10.4171/jems/52

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