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In this paper, we are concerned with a Kirchhoff problem in the presence of astrongly-singular term perturbed by a discontinuous nonlinearity of theHeaviside type in the setting of Orlicz-Sobolev space. The presence of bothstrongly-singular and non-continuous terms bring up difficulties in associatinga differentiable functional to the problem with finite energy in the wholespace $W_0^{1,\Phi}(\Omega)$. To overcome this obstacle, we established anoptimal condition for the existence of $W_0^{1,\Phi}(\Omega)$-solutions to astrongly-singular problem, which allows us to constrain the energy functionalto a subset of $W_0^{1,\Phi}(\Omega)$ to apply techniques of convex analysisand generalized gradient in Clarke sense.

Equivalent conditions for existence of three solutions for a problem with discontinuous and strongly-singular terms