Existence of three solutions for a doubly eigenvalue fourth-order boundary value problem
Afrouz, G. A.
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Afrouz, G. A. Heidarkhani, S.; O’Regan, Donal (2011). Existence of three solutions for a doubly eigenvalue fourth-order boundary value problem. Taiwanese Journal of Mathematics 15 (1), 201-210
In this paper we consider the existence of at least three solutions for the Dirichlet problem u(iv) + alpha u '' + beta u - lambda f(x, u) + mu g(x, u), x is an element of (0, 1) u(0) = u(1) = 0, u ''(0) = u ''(1) = 0 where alpha, beta are real constants, f, g : [0, 1] x R -&gt; R are L(2)-Caratheodory functions and lambda, mu &gt; 0. The approach is based on variational methods and critical points.