Double phase problems with variable growth

By Matija Cencelj, V. Ruadulescu, Dušan D. Repovš. Nonlinear Analysis, 2018

121 citations recorded by the source corpus.

Abstract We consider a class of double phase variational integrals driven by nonhomogeneous potentials. We study the associated Euler equation and we highlight the existence of two different Rayleigh quotients. One of them is in relationship with the existence of an infinite interval of eigenvalues while the second one is associated with the nonexistence of eigenvalues. The notion of eigenvalue is understood in the sense of pairs of nonlinear operators, as introduced by Fucik, Necas, Soucek, and Soucek. The analysis developed in this paper extends the abstract framework corresponding to some standard cases associated to the p ( x ) -Laplace operator, the generalized mean curvature operator, or the capillarity differential operator with variable exponent. The results contained in this paper complement the pioneering contributions of Marcellini, Mingione et al. in the field of variational integrals with unbalanced growth.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9f5c8cbd6c0f3984064b564b9c4b868575ed44f6

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Citations in the corpus

Existence results for double phase implicit obstacle problems involving multivalued operators (2020, unknown): “Works which are closely related to our paper dealing with certain types of double phase problems or multivalued problems can be found in Bahrouni–Rădulescu–Repovš [1],Bahrouni–Rădulescu–Winkert [2,3],Carl–Le-Motreanu [9],Cencelj–Rădulescu–Repovš [10], Clarke [12], Gasiński–Papageorgiou [18,19], Papa”
Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves (2019, unknown): “We also point out the recent paper by Cencelj et al [11] in the framework of double phase problems with variable growth.”
Multiple solutions for parametric double phase Dirichlet problems (2020, background): “Existence and multiplicity results for different types of double phase equations were proved recently by Cencelj-Rˇadulescu-Repovˇs [3], Colasuonno-Squassina [4], Liu-Dai [9] and Rˇadulescu [16].”
Existence and multiplicity of solutions for double‐phase Robin problems (2020, background): “We refer to the very recent works of Bahrouni, Rădulescu and Repovš [1, 2] and the references therein.”
A new class of double phase variable exponent problems: Existence and uniqueness (2021, methodology): “Finally, we refer to some works dealing with existence results for variable exponent problems defined in usual Sobolev spaces with variable exponents, see, for example, Cencelj-Rădulescu-Repovš [17], Gasiński-Papageorgiou [36] and the references therein.”
Existence of solutions for double phase obstacle problems with multivalued convection term (2020, background): “Works which are closely related to ours dealing with certain types of double phase problems can be found in Bahrouni-Rădulescu-Repovš [1], [2], Cencelj-Rădulescu-Repovš [8], Papageorgiou-Rădulescu-Repovš [25], [24], Rădulescu [28] Zhang-Rădulescu [29] and the references therein.”
On the Regularity of Minima of Non-autonomous Functionals (2019, unknown): “3), see for instance [3, 4, 11, 12, 14, 16–22, 48, 51] and [46, 49] for overviews.”
Existence Results for Double Phase Problem in Sobolev–Orlicz Spaces with Variable Exponents in Complete Manifold (2021, background): “For more details, we refer the reader to [3, 10, 13, 16, 15, 21, 18, 23] and the references therein.”
Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold (2020, unknown): “We refer to Bahrouni-Rădulescu-Winkert [3], Cencelj-RădulescuRepovš [12], Marino-Winkert [29], Papageorgiou-Rădulescu-Repovš [35], [36], [37], Rădulescu [42], Zhang-Rădulescu [48], Zeng-Gasiński-Winkert-Bai [46], [47] and the references therein.”