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

2019/01/01 by C. A. M. dos Santos, Laís Vasconcelos Santos, Santos, Carlos Alberto +5 · 1 citation
Computer Science · Mathematics · #35B38 #35D30 #35J20 #35J25 #35J62 #35J75 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1901.00165

openalex publication_date 2019/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 bring up difficulties in associating a differentiable functional to the problem with finite energy in the whole space W₀^1,Φ(Ω). To overcome this obstacle, we established an optimal condition for the existence of W₀^1,Φ(Ω)-solutions to a strongly-singular problem, which allows us to constrain the energy functional to a subset of W₀^1,Φ(Ω) to apply techniques of convex analysis and generalized gradient in Clarke sense.

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