Existence and Nonexistence of Positive Solutions for Singular (p, q)-Equations with Superdiffusive Perturbation

Abstract

We consider a nonlinear Dirichlet problem driven by the (p, q)-Laplacian and with a reaction which is parametric and exhibits the combined effects of a singular term and of a superdiffusive one. We prove an existence and nonexistence result for positive solutions depending on the value of the parameter $$\lambda \in \overset{\circ }{{\mathbb {R}}}_+=(0,+\infty )$$ λ ∈ R ∘ + = ( 0 , + ∞ ) .

Parameter estimates and a uniqueness result for double phase problem with a singular nonlinearity

“…( [1]) proved the existence of two solutions of (4) using the technique of sub-super solutions. In a series of papers ( [11], [12], [13]), Papageorgiou and Winkert have explored bifurcation type results describing the changes in the set of positive solutions of the problem as the parameter λ varies. The reaction term considered in their papers has the combined effects of the singular term as well as a superdiffusive growth term.…”