Publicación: Asymptotically Linear Problems and Antimaximum Principle for the Square Root of the Laplacian
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2016-03-10
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This work deals with bifurcation of positive solutions for some asymptotically linear problems, involving the square root of the Laplacian (-Delta)(1/2). A simplified model problem is the following:
{(-Delta)(1/2)u = lambda m(x)u + g(u) in Omega, u = 0 on partial derivative Omega,
with Omega subset of R-N a smooth bounded domain, N >= 2, lambda > 0, m is an element of L-infinity(Omega), m(+) not equivalent to 0 and g is a continuous function which is super-linear at 0 and sub-linear at infinity. As a consequence of our bifurcation theory approach we prove some existence and multiplicity results. Finally, we also show an anti-maximum principle in the corresponding functional setting.
Descripción
Dedicato ad Antonio Ambrosetti in occasione del suo pensionamento dalla SISSA
Categorías UNESCO
Palabras clave
fractional laplacian, nonlinear problem, bifurcation, antimaximum principle
Citación
Arcoya, David, Colorado, Eduardo and Leonori, Tommaso. "Asymptotically Linear Problems and Antimaximum Principle for the Square Root of the Laplacian" Advanced Nonlinear Studies, vol. 12, no. 4, 2012, pp. 683-701. https://doi.org/10.1515/ans-2012-0402
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Facultades y escuelas::Facultad de Ciencias
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Matemáticas Fundamentales