Isotropic and anisotropic double-phase problems: old and new

By Vicentiu D. Rădulescu. Opuscula Mathematica, 2019

104 citations recorded by the source corpus.

We are concerned with the study of two classes of nonlinear problems driven by differential operators with unbalanced growth, which generalize the \((p,q)\)- and \((p(x),q(x))\)-Laplace operators. The associated energy is a double-phase functional, either isotropic or anisotropic. The content of this paper is in relationship with pioneering contributions due to P. Marcellini and G. Mingione.

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Citations in the corpus

Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves (2019, methodology): “We also point out the abstract setting, respectively the variational analysis developed in the monograph by Rădulescu and Repovš [33] (see also the survey papers [31, 32]).”
A new class of double phase variable exponent problems: Existence and uniqueness (2021, methodology): “[61] V.D. Rădulescu, D.D. Repovš, “Partial Differential Equations with Variable Exponents”, CRC, Boca Raton, 2015.”
Growth conditions and regularity for weak solutions to nonlinear elliptic pdes (2020, unknown): “For related recent references we also quote Duzgun-Marcellini-Vespri [39], [40], Rǎdulescu-Zhang [63], [64], Cencelja-Rădulescu-Repovš [19], Papageorgiou-Rădulescu-Repovš-Dušan [62], Ambrosio-Rădulescu [1], Ragusa-Tachikawa [65], Chlebicka [20], Chlebicka-DeFilippis [21], [22], CupiniGiannetti-Giova”
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 of solutions for double phase obstacle problems with multivalued convection term (2020, background): “Juni 136, 10623 Berlin, Germany a r t i c l e i n f o a b s t r a c t Article history: Received 28 January 2020 Available online 3 March 2020 Submitted by V. Radulescu Keywords: Double phase problems Multivalued convection term Generalized pseudomonotone operators Surjectivity theorem Existence of s”
Constant sign solutions for double phase problems with superlinear nonlinearity (2019, background): “We also refer to the interesting overview article of Rădulescu [24] concerning isotropic and anisotropic double phase problems.”
Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold (2020, unknown): “From Proposition 4.3 and Papageorgiou-Rădulescu-Repovš [38, Theorem 5.7.6] there exist η± ∈ (0, 1) small enough such that ϕ±(0) = 0 inf { ϕ±(0) : ‖u‖1,H = η± }= m±.”