Double phase problems with supercritical and sublinear growth

In this work, our objective is to study the operators involving the nonstandard growth via variational methods. We first study a double phase problem having supercritical growth via minimization technique on convex sets. Alongside, the case of competing <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mo stretchy="false">(</a:mo> <a:mi>p</a:mi> <a:mo>,</a:mo> <a:mi>q</a:mi> <a:mo stretchy="false">)</a:mo> </a:math> Laplacian problems with sublinear growth also has been studied by adopting the variational principle developed for double phase problems.