Abstract
In this note, we study the existence and multiplicity of solutions for the quasilinear elliptic problem as follows: { − div ( a ( | ∇ u | ) ∇ u ) = f ( x , u ) , in Ω ; u = 0 , on ∂ Ω , where Ω⊂ R N is a bounded domain with a smooth boundary. The existence and multiplicity of solutions are obtained by a version of the symmetric mountain pass theorem.
Highlights
In this note, we discuss the existence and multiplicity of solutions of the following boundary value problem: ⎧⎨– div(a(|∇u|)∇u) = f (x, u), in ; ⎩u =, on ∂, ( . )where ⊂ RN is a bounded domain with a smooth boundary ∂
Where ⊂ RN is a bounded domain with a smooth boundary ∂
In Section, we present some preliminary knowledge on the Orlicz-Sobolev spaces and give the main result
Summary
We discuss the existence and multiplicity of solutions of the following boundary value problem: There is a large number of papers on the existence of solutions for the p-Laplacian equation. The second result is that when f (x, t) satisfies < αF(x, t) ≤ tf (x, t), ∀x ∈ , t = , α > p+ and f (x, t) = o(p(|t|)) as |t| → , the problem
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
