A generalization of an extensible beam equation with critical growth inRN

Woinowsky-Krieger, 1950, The effect of axial force on the vibration of hinged bars, J. Appl. Mech., 17, 35, 10.1115/1.4010053 Ball, 1973, Initial–boundary value problems for an extensible beam, J. Math. Anal. Appl., 42, 61, 10.1016/0022-247X(73)90121-2 Ball, 1973, Stability theory for an extensive beam, J. Differential Equations, 14, 399, 10.1016/0022-0396(73)90056-9 Dickey, 1970, Free vibrations and dynamic buckling of the extensible beam, J. Math. Anal. Appl., 29, 443, 10.1016/0022-247X(70)90094-6 Medeiros, 1979, On a new class of nonlinear wave equations, J. Math. Anal. Appl., 69, 252, 10.1016/0022-247X(79)90192-6 Ashfaque, 2012, Invariant boundary value problems for a fourth-order dynamic Euler–Bernoulli beam equation, J. Math. Phys., 53, 043703, 10.1063/1.4711131 Grossinho, 2005, On the solvability of a boundary value problem for a fourth-order ordinary differential equation, Appl. Math. Lett., 18, 439, 10.1016/j.aml.2004.03.011 Kang, 2012, Energy decay of solutions for an extensible beam equation with a weak nonlinear dissipation, Math. Methods Appl. Sci., 35, 1587, 10.1002/mma.2546 Ma, 2010, Global attractor for a model of extensible beam with nonlinear damping and source terms, Nonlinear Anal., 73, 3402, 10.1016/j.na.2010.07.023 Ma, 2003, Existence results and numerical solutions for a beam equation with nonlinear boundary condition, Appl. Numer. Math., 47, 189, 10.1016/S0168-9274(03)00065-5 Ma, 2000, Existence results for a model of nonlinear beam on elastic bearings, Appl. Math. Lett., 13, 189, 10.1016/S0893-9659(00)00026-4 Yang, 2013, On an extensible beam equation with nonlinear damping and source terms, J. Differential Equations, 10.1016/j.jde.2013.02.008 Wang, 2012, Existence and multiplcity of solutions for a fourth-order elliptic equation, Bound. Value Probl., 6, 1 Wang, 2013, Existence of solutions for a fourth order elliptic equation of Kirchhoff type, J. Math. Anal. Appl. Alves, 2012, Nonlinear perturbations of a periodic Kirchhoff equation in RN, Nonlinear Anal., 75, 2750, 10.1016/j.na.2011.11.017 Figueiredo, 2013, Existence of positive solution for a Kirchhoff problem type with critical growth via truncation argument, J. Math. Anal. Appl., 401, 706, 10.1016/j.jmaa.2012.12.053 Lions, 1985, The concentration-compactness principle in the calculus of variations. The limit case, Rev. Mat. Iberoam., 1, 145, 10.4171/RMI/6 Lions, 1984, The concentration-compactness principle in the calculus of variations. The locally compact case. II, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1, 223, 10.1016/s0294-1449(16)30422-x Bernis, 1996, Existence and multiplicity of nontrivial solutions in semilinear critical problems of fourth-order, Adv. Differential Equations, 01, 219, 10.57262/ade/1366896238