Abstract
We consider a Dirichlet problem having a double phase differential operator with unbalanced growth and reaction involving the combined effects of a concave (sublinear) and of a convex (superlinear) terms. We allow the coefficient \(\mathcal E\in L^\infty(\Omega)\) of the concave term to be sign changing. We show that when \(\|\mathcal E\|_\infty \) is small the problem has at least two bounded positive solutions.
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