We consider the boundary value problem, g is a positive weight function and λ is a positive parameter. We derive an estimate for u λ which describes its exact behavior when the parameter λ is large. In general, by invoking appropriate comparison principles, this estimate can be used as a powerful tool in deducing the existence, non-existence and multiplicity of positive solutions of nonlinear elliptic boundary value problems. Here, as an application of this estimate, we obtain a uniqueness result for a nonlinear elliptic boundary value problem with a singular nonlinearity.
In this paper we prove a strong comparison principle for radially decreasing solutions u, v ∈ C 1,α 0 ( BR ) of the singular equationsHere we assume that 1 < p < 2, δ ∈ (0, 1) and f, g are continuous, radial functions such that 0 ≤ f ≤ g but f ≡ g in B R . For the case p > 2 a counterexample is provided where the strong comparison principle is violated. As an application of strong comparison principle, we prove a three solution theorem for p-Laplace equation and illustrate with an example.
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