Multiple solutions for parametric double phase Dirichlet problems

By Nikolaos S. Papageorgiou, Calogero Vetro, Francesca Vetro. Communications in Contemporary Mathematics, 2020

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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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/569e0c757a85986ba2640a2faa77f1b828836b7e

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Existence and multiplicity of solutions for double‐phase Robin problems (2020, background): “nd Dai [13] (existence of solutions for problems with superlinear reaction), Papageorgiou, Ra˘dulescu and Repovˇs [19] (multiple solutions for superlinear problems), and Papageorgiou, Vetro and Vetro [20] (parametric Dirichlet problems). The approach in all the aforementioned works is diﬀerent and t”