For a Kirchhoff equation with indefinite data, the paper characterizes positive solvability through an auxiliary linear problem, showing existence, multiplicity, uniqueness, and nonexistence depending on the exponent and parameter lambda.
Azzollini, The elliptic Kirchhoff equation in RN perturbed by a local nonlin- earity, Differential Integral Equations, 25 (2012), 543-554
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Positive solutions of inhomogeneous Kirchhoff type equations with indefinite data
For a Kirchhoff equation with indefinite data, the paper characterizes positive solvability through an auxiliary linear problem, showing existence, multiplicity, uniqueness, and nonexistence depending on the exponent and parameter lambda.