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Abstract. The classical maximum principle is utilized to obtain maximum principles for functionals which are defined on solutions of fourth, sixth and eighthorder elliptic equations. The principles derived lead to uniqueness results.2000 Mathematics Subject Classification. 35J40, 35B50.

This note is concerned with the problem of existence and uniqueness of solutions for a fourth order boundary value problem that models the deflection of a hinged plate of nonconstant thickness.

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This paper is concerned with the problem of existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem. The existence and uniqueness for weak solutions follows from standard variational methods, while similar uniqueness results for classical solutions are derived using maximum principles. doi:10.1017/S1446181119000129