Ontology type: schema:ScholarlyArticle
2019-01
AUTHORS ABSTRACTWe study the multiplicity of concentrating solutions to the nonlinear fractional Kirchhoff equation ε2sa+ε4s-3b∫R3|(-Δ)s2u|2dx(-Δ)su+V(x)u=f(u)inR3,where ε>0 is a positive parameter, (-Δ)s is the fractional laplacian with s∈(34,1),a,b are positive constants, and V is a positive potential such that inf∂ΛV>infΛV for some open bounded subset Λ⊂R3. We relate the number of positive solutions with the topology of the set where V attains its minimum in Λ. The proof is based on the Ljusternik–Schnirelmann theory. More... »
PAGES159-203
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DOIhttp://dx.doi.org/10.1007/s00229-018-1017-0
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