Multiple Solutions for a Nonlinear Dirichlet Problem via - Mathematics
Multiple Solutions for a Nonlinear Dirichlet Problem via - Mathematics
Multiple Solutions for a Nonlinear Dirichlet Problem via - Mathematics
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Theorem A. If f satisfies (f1), (f2), (f3), k ≥ 4 is an even number, and all<br />
the solutions of (0.1) are nondegenerate then problem (0.1)<br />
has at least five solutions: u1 = 0, u2 > 0 in Ω, u3 < 0 in Ω, u4, and u5.<br />
Moreover,<br />
(a) m(u4,J) = k.<br />
(b) u5 changes sign, m(u5,J) is even and m(u5,J) ≤ k.<br />
MULTIPLE SOLUTIONS FOR A NONLINEAR DIRICHLET PROBLEM VIA MORSE INDEX – 10➲<br />
▲ ▲<br />
➲ ❏ ✘