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We study parametric double phase problems involving superlinearnonlinearities with a growth that need not necessarily be polynomial. Based ontruncation and comparison methods the existence of two constant sign solutionsis shown provided the parameter is larger than the first eigenvalue of the$p$-Laplacian. As a result of independent interest we prove a priori estimatesfor solutions for a general class of double phase problems with convectionterm.

Constant sign solutions for double phase problems with superlinear nonlinearity