On the Morse indices of sign changing solutions of nonlinear elliptic problems

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On a superlinear elliptic p-Laplacian equation (2004, result): “In particular, we generalize the above mentioned results from [1, 2, 4, 6, 8, 16, 17, 21] on the”
A note on additional properties of sign changing solutions to superlinear elliptic equations (2003, background): “If (A1)–(A3) hold and f is odd in u, then every weak solution u ∈ E of (1.1) with 0 Φ(u) ≤ βn has at most n nodal domains.”
Ljusternik-Schnirelman theory in partially ordered Hilbert spaces (2002, methodology): “This is related to the notion of X-regularity as used in [33] and [15], and similar ideas were used also in [8], [ 9 ], [10], [16], [26].”
Sign Changing Solutions of Superlinear Schrödinger Equations (2003, methodology): “We believe that this approach to estimate the number of nodal domains is more useful and more elementary than the one using the Morse index (as in [9] or [3]).”
Critical Point Theory on Partially Ordered Hilbert Spaces (2001, result): “5 which is due to [6].”
Nodal Solutions of a p‐Laplacian Equation (2005, background): “The systematic investigation of nodal properties of solutions, based on new variational methods in ordered Hilbert spaces, has found increasing interest recently; see [5, 6, 9, 10, 12, 16, 19 21, 28 30, 32, 33] and the references therein.”