Discontinuous perturbations of nonhomogeneous strongly-singular Kirchhoff problems

Abstract In this paper, we are concerned with a Kirchhoff problem in the presence of strongly-singular term perturbed by discontinuous nonlinearity Heaviside type setting Orlicz–Sobolev space. The both and non-continuous terms brings up difficulties associating differentiable functional to finite energy whole space $$W_0^{1,\Phi }(\Omega )$$ W 0 1 , Φ ( Ω ) . To overcome obstacle, establish an optimal condition for existence -solutions problem, which allows us constrain subset order apply techniques convex analysis generalized gradient sense Clarke.