Abstract
A variety of three-critical-point theorems have been established for non-smooth functionals, based on a minimax inequality. In this paper, a generalized form of a recent result due to Ricceri is introduced for non-smooth functionals and by a few hypotheses, without any minimax inequality, the existence of at least three critical points with a uniform bound on the norms of solutions, is obtained. Also, as an application, our main theorem is used to obtain at least three anti-periodic solutions for a second order differential inclusion.
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The authors would like to thank the anonymous reviewer for his/her helpful feedback and valuable suggestions which led to an improvement in the quality of their paper.
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AFROUZI, G.A., GHAEMI, M.B. & MIR, S. A three critical point theorem for non-smooth functionals with application in differential inclusions. Proc Math Sci 125, 521–535 (2015). https://doi.org/10.1007/s12044-015-0249-0
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DOI: https://doi.org/10.1007/s12044-015-0249-0