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

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Positive solutions for a weakly coupled nonlinear Schrödinger system (2006, methodology): “We will first use an argument similar to the proof of Theorem 4.5 in [ 21 ] in order to show thatm, defined as m = inf{I(w);w 6= 0 and I0(w) = 0},”
Solvability of Uniformly Elliptic Fully Nonlinear PDE (2010, unknown): “For nonlinearities similar to f(v) in (21), some related problems have been studied in [J], [ JT ].”
Schrödinger equations with concave and convex nonlinearities (2005, result): “For a radially symmetric Schr¨ odinger equation with an asymptotically linear term, one radial solution has been obtained in [36, 38] by Stuart and Zhou and their results were generalized to more general situations in [15, 21, 22 , 25]; even if the globally superlinear assumption was not needed, th”
Global Branch of Solutions for Non‐Linear Schrödinger Equations with Deepening Potential Well (2006, background): “The existence results in [14] and [15] are based on concentration–compactness arguments and the fact that the mountain pass geometry occurs for the associated energy functional due to (i) and (ii).”