FRACTIONAL LOGARITHMIC DOUBLE PHASE PROBLEMS: QUALITATIVE ANALYSIS IN THE ANISOTROPIC CASE

FRACTIONAL LOGARITHMIC DOUBLE PHASE PROBLEMS: QUALITATIVE ANALYSIS IN THE ANISOTROPIC CASE

Článek WoS

This paper is concerned with the study of elliptic differential problems involving fractional variable exponent double phase operators with logarithmic perturbation (-\Delta)s \scrH generated by \scrH(x, y, t) = [tp(x,y) p(x,y) +\mu(x, y) tq(x,y) q(x,y) ] log(e+\alphat). In the first part, we study fractional double phase elliptic inclusions with a generalized multivalued mapping and a maximal monotone operator which is formulated by the convex subdifferential of the indicator function to a convex set. Based on the subsupersolution method along with truncation techniques and nonsmooth analysis we show an existence result and give an application construction such a pair of sub-supersolution. Additionally, under lattice conditions, we establish the compactness and the directedness of the solution set within a pair of suband supersolutions. In the second part, we consider a type of fractional Kirchhoff double phase problems governed by the operator (-\Delta)s\scrH. Applying variational methods, the Poincare'\--Miranda existence theorem together with the quantitative deformation lemma, we prove a multiplicity result which says that the problem has at least a positive solution, a negative solution, and a sign-changing solution.

This paper is concerned with the study of elliptic differential problems involving fractional variable exponent double phase operators with logarithmic perturbation (-\Delta)s \scrH generated by \scrH(x, y, t) = [tp(x,y) p(x,y) +\mu(x, y) tq(x,y) q(x,y) ] log(e+\alphat). In the first part, we study fractional double phase elliptic inclusions with a generalized multivalued mapping and a maximal monotone operator which is formulated by the convex subdifferential of the indicator function to a convex set. Based on the subsupersolution method along with truncation techniques and nonsmooth analysis we show an existence result and give an application construction such a pair of sub-supersolution. Additionally, under lattice conditions, we establish the compactness and the directedness of the solution set within a pair of suband supersolutions. In the second part, we consider a type of fractional Kirchhoff double phase problems governed by the operator (-\Delta)s\scrH. Applying variational methods, the Poincare'\--Miranda existence theorem together with the quantitative deformation lemma, we prove a multiplicity result which says that the problem has at least a positive solution, a negative solution, and a sign-changing solution.

fractional logarithmic double phase operator; multivalued problem; sub-supersolution method; nonsmooth analysis; Kirchhoff-type problem; variational methods

fractional logarithmic double phase operator; multivalued problem; sub-supersolution method; nonsmooth analysis; Kirchhoff-type problem; variational methods

ZHENG, S.; LU, Y.; RADULESCU, V.; WINKERT, P.

15.05.2026

SIAM journal on mathematical analysis

58

3

Spojené státy americké

2323

2374

52

https://www.webofscience.com/wos/woscc/full-record/WOS:001761838100009