Combinatorics

Physics

Dirichlet distribution

Pure mathematics

Mathematics

Truncation (statistics)

Parametric statistics

Statistics

Sign (mathematics)

Mathematical analysis

Boundary value problem

Spectrum (functional analysis)

Programming language

Constant (computer programming)

Dirichlet problem

Computer science

Quantum mechanics

Applied mathematics

Communications in Contemporary Mathematics

We consider a parametric double phase Dirichlet problem. Using variational tools together with suitable truncation and comparison techniques, we show that for all parametric values [Formula: see text] the problem has at least three nontrivial solutions, two of which have constant sign. Also, we identify the critical parameter [Formula: see text] precisely in terms of the spectrum of the [Formula: see text]-Laplacian.

Multiple solutions for parametric double phase Dirichlet problems