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Least energy sign-changing solution for logarithmic double phase problems with nonlinear boundary condition

delete2025-09-16
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F
Franziska Borer *
L
Leszek Gasiński
M
Matheus F. Stapenhorst
P
Patrick Winkert
DOI：10.1007/s00526-025-03079-2delete
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Abstract

Abstract

En 中文
In this paper we study logarithmic double phase problems with superlinear right-hand sides and nonlinear Neumann boundary condition. In particular, we show that the problem under consideration has a least energy sign-changing solution. The proof is based on the minimization of the energy functional over the related nodal Nehari manifold along with the Poincar & eacute;-Miranda existence theorem. As a result of independent interest, we prove the existence of a new and very general equivalent norm in the logarithmic Musielak-Orlicz Sobolev space. In addition, we present a priori bounds for a large class of logarithmic double phase problems involving convection terms for critical and subcritical situations.
Keywords:
IMPLICIT OBSTACLE PROBLEMS
ELLIPTIC-EQUATIONS
MINIMIZERS
REGULARITY
EXISTENCE
FUNCTIONALS
INTEGRALS
CALCULUS
ROBIN
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Journal

C
Calculus of Variations and Partial Differential Equations
IF:
2
Papers:
247
Citations:
0

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