Positive solutions for nonlinear nonhomogeneous Dirichlet problems with concave-convex nonlinearities

(p, q)-Equations with Singular and Concave Convex Nonlinearities

“…More recently there have been generalizations involving more general nonlinear differential operators, more general concave and convex nonlinearities and different boundary conditions. We refer to the works of Papageorgiou-Rȃdulescu-Repovš [23] for Robin problems and Papageorgiou-Winkert [19], Leonardi-Papageorgiou [14] and Marano-Marino-Papageorgiou [16] for Dirichlet problems. None of these works involves a singular term.…”

(p, 2)-Equations with a Crossing Nonlinearity and Concave Terms

“…On account of hypotheses H 1 (i), (iv) we can find c 15 > 0 such that (23) F (z, x) ≤ c 15 [|x| q + |x| r + ] for a.a. z ∈ Ω and all x ∈ R.…”

“…Since then appeared several works with further generalizations. Just to quote a few we mention the works of Gasiński-Papageorgiou [9,10], Papageorgiou-Repovš-Vetro [18,19], Papageorgiou-Vetro-Vetro [20,21], Papageorgiou-Winkert [23], and the recent papers of Papageorgiou-Qin-Rȃdulescu [12] and Papageorgiou-Rȃdulescu-Repovš [15] on anisotropic equations. In all these works the concave term enters in the equation with a positive sign and this permits the use of the strong maximum principle which provides more structural information concerning the solution.…”

(p,q)-Equations with singular and concave convex nonlinearities

“…More recently there have been generalizations involving more general nonlinear differential operators, more general concave and convex nonlinearities and different boundary conditions. We refer to the works of Papageorgiou-Rȃdulescu-Repovš [21] for Robin problems and Papageorgiou-Winkert [24], Leonardi-Papageorgiou [14] and Marano-Marino-Papageorgiou [16] for Dirichlet problems. None of these works involves a singular term.…”