Existence of Nontrivial Solutions of a Two Point Boundary Value Problem for a 2nth Order Nonlinear Difference Equation
نویسندگان
چکیده
We will show how to use the mountain pass theorem to obtain nontrivial solutions of a certain two point BVP for the 2nth order, n ∈ N (formally) self-adjoint nonlinear difference equation n ∑ i=0 [ri(t) u(t − i)] = f (t, u(t)), t ∈ [a, b]Z. No periodicity assumptions will be placed on ri, i = 0, 1, . . . , n or f and it will be assumed that f grows superlinearly both at the origin and at infinity. An example of our results will be given. AMS subject classification: 39A10.
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