Existence and local boundedness of solutions of a -Laplacian problem. Issue 4 (12th March 2019) - Arriagada, Waldo; Huentutripay, Jorge
ABSTRACT: In this paper, we consider theϕ -Laplacian equation- div ϕ ( | ∇ u | ) ∇ u / | ∇ u | = λ g ( · ) ϕ ( u ) in R N whereϕ is an odd increasing homeomorphism fromR ontoR which is not necessarily differentiable. The termλ is a suitable parameter and g is measurable. We prove that nontrivial and nonnegative weak solutions of this equation exist. The problem on the local boundedness of the solutions is also treated. Mild restrictions are imposed on g andϕ .