Discontinuous perturbations of nonhomogeneous strongly-singular Kirchhoff problems

Autor: Carlos Alberto Santos, Lais Santos, Marcos L. M. Carvalho, Vicenţiu D. Rădulescu
Rok vydání: 2021
Předmět:
Zdroj: Nonlinear Differential Equations and Applications NoDEA. 28
ISSN: 1420-9004
1021-9722
DOI: 10.1007/s00030-021-00730-7
Popis: In this paper, we are concerned with a Kirchhoff problem in the presence of a strongly-singular term perturbed by a discontinuous nonlinearity of the Heaviside type in the setting of Orlicz–Sobolev space. The presence of both strongly-singular and non-continuous terms brings up difficulties in associating a differentiable functional to the problem with finite energy in the whole space $$W_0^{1,\Phi }(\Omega )$$ W 0 1 , Φ ( Ω ) . To overcome this obstacle, we establish an optimal condition for the existence of $$W_0^{1,\Phi }(\Omega )$$ W 0 1 , Φ ( Ω ) -solutions to a strongly-singular problem, which allows us to constrain the energy functional to a subset of $$W_0^{1,\Phi }(\Omega )$$ W 0 1 , Φ ( Ω ) in order to apply techniques of convex analysis and generalized gradient in the sense of Clarke.
Databáze: OpenAIRE