Double-phase problems and a discontinuity property of the spectrum

Abstract

We consider a nonlinear eigenvalue problem driven by the sum of $p$ and $q$-Laplacian. We show that the problem has a continuous spectrum. Our result reveals a discontinuity property for the spectrum of a parametric ($p,q$)-differential operator as the parameter $\beta \to 1^{-}$.

References in corpus (3)

• Double-phase problems with reaction of arbitrary growth
• $(p,2)$-equations asymmetric at both zero and infinity
• Existence and multiplicity of solutions for resonant $(p,2)$-equations

Cited by in corpus (8)

• Ground state and nodal solutions for a class of double phase problems
• Anisotropic equations with indefinite potential and competing nonlinearities
• Nonvariational and singular double phase problems for the Baouendi-Grushin operator
• Anisotropic singular Neumann equations with unbalanced growth
• Robin double-phase problems with singular and superlinear terms
• Unbalanced fractional elliptic problems with exponential nonlinearity: subcritical and critical cases
• Unbalanced $(p,2)$-fractional problems with critical growth
• Sobolev and Hölder regularity results for some singular nonhomogeneous quasilinear problems