Constant sign solutions for double phase problems with superlinear nonlinearity

TL;DR

This paper establishes the existence of two constant sign solutions for parametric double phase problems with superlinear nonlinearities, using truncation and comparison methods, and provides a priori estimates for solutions.

Contribution

It introduces new existence results for double phase problems with superlinear growth and develops a priori estimates for a broad class of such problems.

Findings

Existence of two constant sign solutions when parameter exceeds the first eigenvalue.

Solutions can be obtained via truncation and comparison methods.

A priori estimates are established for solutions with convection terms.

Abstract

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