Abstract
In this paper, we consider the following p-Laplacian equation in R+N with critical boundary nonlinearity. The existence of infinitely many solutions of the equation is proved via the truncation method.
Highlights
In this paper, we consider the following p-Laplacian equation in R+boundary nonlinearity N− ∆ p u = 0, in R+|∇u| p−2 ∂u + |u| p−2 u = |u| p−2 u + μ|u|q−2 u,∂n where 1 < p < N, max{ p, p − 1} < q < p = ∆pu =div(|∇u| p−2 ∇u). ( N −1) pN− p, on R N −1 = ∂R+ (1)
N by x = ( y, s ) ∈ R N −1 × [0, ∞ ) and we identify the form u( x ) = u(|y|, s), where we denote x ∈ R+
All of these authors found the solutions as limits of approximated equations with subcritical growth in bounded domains
Summary
All of these authors found the solutions as limits of approximated equations with subcritical growth in bounded domains. In order to show the existence of multiple solutions of the original problems, we need to check that multiple solutions of approximated problems do not converge to the same solution of the limit problems By a concentration–compactness analysis, similar to that in [2,3,7], in particular with use of a local Pohožaev identity, the theorem of convergence of approximate solutions is proved. We prove the existence Theorem 2 by showing that approximated solutions are solutions of the original problem for a sufficiently small parameter
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.
