Abstract
We consider a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a \begin{document}$p$\end{document} -Laplacian and a Laplacian and a reaction term which is \begin{document}$(p-1)$\end{document} -linear near \begin{document}$\pm \infty$\end{document} and resonant with respect to any nonprincipal variational eigenvalue of \begin{document}$(-\Delta_p,W^{1,p}_0(\Omega))$\end{document} . Using variational tools together with truncation and comparison techniques and Morse Theory (critical groups), we establish the existence of six nontrivial smooth solutions. For five of them we provide sign information and order them.
Highlights
Let Ω ⊆ RN be a bounded domain with a C2-boundary ∂Ω
Using variational tools together with truncation and comparison techniques and Morse Theory, we establish the existence of six nontrivial smooth solutions
In this paper we study the following nonlinear nonhomogeneous Dirichlet problem
Summary
Let Ω ⊆ RN be a bounded domain with a C2-boundary ∂Ω. In this paper we study the following nonlinear nonhomogeneous Dirichlet problem. Using variational tools (critical point theory), together with truncation techniques and Morse theory (critical groups), we show that the problem has at least six nontrivial smooth solutions. For five of these solutions we provide sign information and order them. None of the aforementioned works treats problems resonant at higher parts of the spectrum or produces six nontrivial smooth solutions with sign and order information. {φ(un)}n∈N ⊆ R is bounded, (1 + un )φ (un) → 0 in X∗ as n → +∞, admits a strongly convergent subsequence” This compactness-type condition on φ, leads to a deformation theorem, from which one can derive the minimax theory for the critical values of φ.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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 call
