By Ivar Ekeland, Roger Témam
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2) are used to prove that they are the same. 45). 45) be the fixed points of a certain completely continuous operator, and then, to apply the Schauder fixed point theorem . 55) R ! x/j; 8 y 2 X x2Œ0;L x2Œ0;L we can define the operator T W X ! X/ is bounded. 45). X/ is not bounded, there would exist a sequence fyn g X such that kuyn kX ! 1: Moreover, from the hypotheses of the theorem, the sequence of functions fb. ; yn . 0; L/ and, passing to a subsequence if necessary, we may assume that fb.
108, 152–169 (1994) 18. : Neumann boundary value problems for second-order ordinary differential equations across resonance. SIAM J. Control Optim. 33, 1312–1325 (1995) 19. : On Lyapunov’s inequality for disfocality. J. Math. Anal. Appl. 83, 486–494 (1981) 20. : Linear eigenvalues and a nonlinear boundary value problem. Pac. J. Math. 33, 311–328 (1970) 21. : Second order Neumann boundary value problems across resonance. ESAIM Control Optim. Calc. Var. 12, 398–408 (2006) 22. : Problème général de la stabilité du mouvement.
0; 1/ of positive measure. 2 on Œ0; 1 and Conditions of this type are referred to as nonuniform nonresonance conditions with respect to the first positive eigenvalue of the associated linear homogeneous problem. 45). 1). 45). 2). , none of these hypotheses implies the other). 9) and studies the limits of kˇkp for p ! 1C and p ! 1 (see  for further details). 4. 45) where the following requirements are fulfilled: 1. f and fu are continuous on Œ0; L R: 2. x; u/ in Œ0; L R. e. x; 0/ dx D 0: 0 3.