‎Using Nehari manifold methods and Mountain pass theorem‎, ‎the existence of nontrivial and radially symmetric solutions for a class of $p$-Kirchhoff-type system are established.

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Variational methods find solutions of equations by considering a solution as a critical point of an appropriately chosen function. Local minima and maxima are well-known types of critical points. We explore methods for finding critical points that are neither local maxima or minima, but instead are mountain passes or saddle points. Criteria for the existence of minima or maxima are well-known, ...

We will show how to use the mountain pass theorem to obtain nontrivial solutions of a certain two point BVP for the 2nth order, n ∈ N (formally) self-adjoint nonlinear difference equation n ∑ i=0 [ri(t) u(t − i)] = f (t, u(t)), t ∈ [a, b]Z. No periodicity assumptions will be placed on ri, i = 0, 1, . . . , n or f and it will be assumed that f grows superlinearly both at the origin and at infini...

We consider P 0 nonlinear complementarity problems and study the con-nectedness and stability of the solutions by applying degree theory and the Mountain Pass Theorem to a smooth reformulation of the complementarity problem. We show that the solution set is connected and bounded if a bounded isolated component of the solution set exists and that a solution is locally unique if and only if it is...

{ In this note we present a general mountain pass principle dropping any smoothness or even continuity assumptions on the functional. As a corollary, we prove existence of a point with an arbitrarily xed small slope if the "low" part of the "barrier" is suuciently far from the "boundary", obtaining in addition estimates for the location of the point.

We revisit the classical problem of the buckling of a long thin axially compressed cylindrical shell. By examining the energy landscape of the perfect cylinder, we deduce an estimate of the sensitivity of the shell to imperfections. Key to obtaining this estimate is the existence of a mountain pass point for the system. We prove the existence on bounded domains of such solutions for almost all ...

Let G = (V, E) be a locally finite graph, Ω ⊂ V be a bounded open domain, ∆ be the usual graph Laplacian, and λ1(Ω) be the first eigenvalue of −∆ with respect to Dirichlet boundary condition. Using the mountain pass theorem of Ambrosette and Rabinowitz, We prove that if α < λ1(Ω), then for any p > 2, there exists a positive solution to  −∆u − αu = |u| p−2u in Ω◦, u = 0 on ∂Ω, where Ω◦ and...