Existence results for a class of second order differential equations with nonlinear derivative dependence
Abstract:We establish multiplicity results for nontrivial solutions of the quasilinear second order differential equation on afor 1 ≤ i ≤ n, under appropriate hypotheses. Indeed, using a consequence of the local minimum theorem due to Bonanno and, the mountain pass theorem, we investigate the existence of two solutions for the problem under some algebraic conditions with the classical Ambrosett-Rabinowitz condition on the nonlinear terms. Moreover, by combining two algebraic conditions on the nonlinear terms, and emplo… Show more
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