Applying the mountain pass theorem to an asymptotically linear elliptic equation on R^N

Positive solutions for asymptotically linear problems in exterior domains

“…The problem (2.7) has a positive, radially symmetric, least action solution (whose existence is proved in [10,36] for N ≥ 3 and in [11] for N = 2. ), which we denote with w. In [34] it is shown the uniqueness of w when f satisfies the additional hypothesis…”

“…where the second inequality is assumed in order to have a solution of the problem in the whole N (see [10,11,36]). When dealing with this kind of non-linearities it is often assumed a non-quadraticity type condition (introduced in [21])…”

A positive solution for an asymptotically linear elliptic problem on $\mathbb{R}^N$ autonomous at infinity

“…Subsequently, taking advantages of some techniques introduced in [7], an extended study of radially symmetric problems on R N was done in [12]. Finally we wish to mention [13] where a first order Hamiltonian system with an asymptotically linear part is studied.…”

A Dirichlet problem with asymptotically linear and changing sign nonlinearity

“…Let us finally mention that problem (1.1) has been recently studied also on R N in [26], [23], [19], [20], assuming in an essential way that g has to be positive.…”