Existence of a continuum of solutions for a quasilinear elliptic singular problem
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URI: http://hdl.handle.net/10835/15650
DOI: https://doi.org/10.1016/j.jmaa.2015.12.034
DOI: https://doi.org/10.1016/j.jmaa.2015.12.034
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2016Resumen
In this paper we study the existence of positive solution u ∈ H1 0 (Ω) for some quasilinear elliptic equations, having lower order terms with quadratic growth in the gradient and singularities, whose model is
−∆u + µ(x) |∇u| 2 u γ + u β = λup + f0(x), x ∈ Ω, 0 < γ ≤ β, 0 < p.
Using topological methods we obtain the existence of an unbounded continuum of solutions. In the case µ(x) constant we derive the existence of solution for every λ > 0 if 1 < γ < 2 for any β and p < 1. Even more for µ ∈ L∞(Ω) we prove this result if β ≤ 1 and p < 2 − β.
Palabra/s clave
Continua of solutions
Nonlinear elliptic equations
Singular lower order term with quadratic growth