Multiplicity of solutions for p ( x ) -polyharmonic elliptic Kirchhoff equations

By Francesca Colasuonno, Patrizia Pucci. 2011

261 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/03500cbd97de87ec6918578b33aee3674d92694f

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

On a fractional degenerate Kirchhoff-type problem (2017, background): “We also mention, for the sake of completeness, that degenerate Kirchhofftype problems driven by non-homogeneous elliptic operators have been recently taken into account, for instance, in [13, 14, 15, 17, 34, 35].”
On the existence of stationary solutions for higher-order p-Kirchhoff problems (2014, methodology): “A preliminary study of ∆p only when d = 1 has been first developed in [1], where a possibly degenerate scalar stationary p–polyharmonic Kirchhoff Dirichlet problem has been considered.”
Multiplicity results for the non-homogeneous fractional p-Kirchhoff equations with concave–convex nonlinearities (2015, methodology): “Note that assumption (M) is used to get the multiplicity of solutions of a class of higher-order p(x)Kirchhoff equations in [33].”
MOUNTAIN PASS SOLUTIONS FOR NONLOCAL EQUATIONS (2014, methodology): “[9] Autuori, G., and P. Pucci: Kirchhoff systems with nonlinear source and boundary damping terms.”
Existence theorems for entire solutions of stationary Kirchhoff fractional p-Laplacian equations (2016, background): “As note in [9], condition (M1) gives that M(t) > 0 for any t > 0.”
Kirchhoff–Hardy Fractional Problems with Lack of Compactness (2017, background): “In particular, to handle the Kirchhoff coefficient on a degenerate setting we need appropriate lower and upper bounds for M, given by (M1) and (M2), which first appear in [8].”
Existence of solutions for Kirchhoff type problem involving the non-local fractional p-Laplacian (2015, background): “In [10], the authors investigated higher order p(x)-Kirchhoff type equations via symmetric Mountain Pass Theorem, even in the degenerate case.”
Infinitely many solutions for a fractional Kirchhoff type problem via Fountain Theorem (2015, methodology): “For example, we refer to [13] for non-degenerate Kirchhoff type problems and [12,11] for degenerate Kirchhoff type problems.”
Existence of solutions for fourth order elliptic equations of Kirchhoff type (2014, unknown): “For example, in [1, 5, 6, 15], the authors studied the existence of positive solutions of second order non-degenerate Kirchhofftype problems; in [4], F.”