MULTIPLICITY OF POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC P-LAPLACIAN SYSTEMS

作者：Aghajani Asadollah^*; Shamshiri Jamileh

来源：Electronic Journal of Differential Equations, 2012, 111.

• Critical points
• nonlinear boundary value problems
• quasilinear p-Laplacian problem
• fibering map
• Nehari manifold

We study the existence and multiplicity of solutions to the elliptic system
-div(vertical bar del u vertical bar(p-2)del u) + m(1)(x)vertical bar u vertical bar(p-2)u = lambda g(x, u) x is an element of Omega,
-div(vertical bar del v vertical bar(p-2)del v) + m(2)(x)vertical bar v vertical bar(p-2)v = mu h(x, v) x is an element of Omega,
vertical bar del u vertical bar(p-2)partial derivative u/partial derivative n = f(u)(x, u, v), vertical bar del v vertical bar(p-2)partial derivative v/partial derivative n = f(v)(x, u, v),
where Omega subset of R-N is a bounded and smooth domain. Using fibering maps and extracting Palais-Smale sequences in the Nehari manifold, we prove the existence of at least two distinct nontrivial nonnegative solutions.

• 出版日期2012-7-2