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In this paper, a fourth-order nonlinear difference equation is considered. By making use of the critical point theory, we establish various sets of sufficient conditions for the existence and nonexistence of solutions for Neumann boundary value problem and give some new results. Results obtained generalize and complement the existing ones.

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Abstract  

We study a class of submanifolds, called Generalized Cauchy-Riemann (GCR) lightlike submanifolds of indefinite Sasakian manifolds as an umbrella of invariant, screen real, contact CR lightlike subcases [8] and real hypersurfaces [9]. We prove existence and non-existence theorems and a characterization theorem on minimal GCR-lightlike submanifolds.

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and nonexistence of positive entire solutions of second order semilinear elliptic systems, Funkcial. Ekvac. 42 (1999), 241-260. MR 2001i :35051 Existence and nonexistence of positive entire solutions of second order

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. France , 93 ( 1965 ), 97 – 107 . [4] Saoudi , K. , Existence and non-existence of solution for a singular problem with

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