Logarithmic double phase problems with critical growth on the boundary

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ÖZTÜRK E., Winkert P.

Journal of Elliptic and Parabolic Equations, 2026 (ESCI, Scopus)

• Publication Type: Article / Article
• Publication Date: 2026
• Doi Number: 10.1007/s41808-026-00446-8
• Journal Name: Journal of Elliptic and Parabolic Equations
• Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
• Keywords: Critical growth on the boundary, Equivalent norm, Logarithmic double phase operator, Sign-changing solutions, Steklov eigenvalue problem, Symmetric mountain pass theorem
• Hacettepe University Affiliated: Yes

Abstract

In this paper, we study logarithmic double phase problems with critical growth on the boundary of the form (Formula presented.) where divL stands for the logarithmic double phase operator given by (Formula presented.) e is Euler’s number, ν(x) is the outer unit normal of Ω at x∈∂Ω, Ω⊂RN, N≥2, is a bounded domain with Lipschitz boundary ∂Ω, 10 is a Carathéodory function, just locally defined with a specific behavior near the origin. Using suitable truncation methods and an appropriate auxiliary problem along with an equivalent norm in our function space, we establish the existence of an entire sequence of sign-changing solutions to the above problem, which converges to zero in both the logarithmic Musielak-Orlicz Sobolev space W1,Hlog(Ω) and in L∞(Ω).