Constant sign and nodal solutions for parametric (<i>p</i>, 2)-equations

Abstract

the work of Zhikov [2] who used (p, )-equations to describe phenomena in nonlinear elasticity. More precisely, Zhikov introduced models for strongly anisotropic materials in the context of homogenization. For this purpose Zhikov introduces the so-called double phase functional Jp,q(u) = |Du| p + a(z)|Du| q dz with a(z) M for a.a. z , < q < p, u W ,p (). Here the modulating coe cient a(z) dictates the geometry of the composite made of two di erent materials with hardening exponents p and q respectively.