A new augmented singular transform and its partial Newton-correction method for finding more solutions to nonvariational quasilinear elliptic PDEs

Chen, 2015, Estimate of Morse index of cooperative elliptic systems and its application to spatial vector solitons, J. Comput. Appl. Math., 281, 169, 10.1016/j.cam.2014.11.046 Costa, 2001, A numerical investigation of sign-changing solutions to superlinear elliptic equations on symmetric domains, J. Comput. Appl. Math., 131, 299, 10.1016/S0377-0427(00)00266-1 Ganesh, 1993, A BIE method for a nonlinear BVP, J. Comput. Appl. Math., 45, 299, 10.1016/0377-0427(93)90047-F Henkelman, 2000, Methods for finding saddle points and minimum energy paths, vol. 5 Lin, 1987, Computing multiple solutions to systems of interlinked separation columns, AIChE J., 6, 886, 10.1002/aic.690330603 Musslimani, 2000, Composite multihump vector solitons carrying topological charge, Phys. Rev. Lett., 84, 1164, 10.1103/PhysRevLett.84.1164 Yao, 2018, Two classes of Ljusternik–Schnirelman minimax algorithms and an application for finding multiple negative energy solutions of a class of p-Laplacian equations, J. Comput. Appl. Math., 342, 495, 10.1016/j.cam.2018.04.020 Clement, 2000, Existence of positive solutions for a nonvariational quasilinear elliptic system, J. Differential Equations, 166, 455, 10.1006/jdeq.2000.3805 Fethi, 2016, Existence of solutions for a non-variational system of elliptic PDE’s via topological methods, Electron. J. Differential Equations, 13, 35 Motreanu, 2018, Multiple solutions for nonvariational quasilinear elliptic systems, Mediterr. J. Math., 88, 1 Idir, 2018, Existence of solutions of a non-variational bi-harmonic system via fixed point theory, Filomat, 32, 4113, 10.2298/FIL1812113M Badiale, 2001, Concentrated solutions for a non variational semilinear elliptic equation, Houston J. Math., 27, 649 Brown, 1971, Deflation techniques for the calculation of further solutions of a nonlinear system, Numer. Math., 16, 334, 10.1007/BF02165004 Yang, 2008, Bifurcation method for solving multiple positive solutions to Henon equation, Sci. China A, 51, 2330, 10.1007/s11425-007-0198-x Neuberger, 2001, Newton’s method and morse index for semilinear elliptic PDEs, Int. J. Bifurcation Chaos, 11, 801, 10.1142/S0218127401002444 Wang, 2004, A local minimax-Newton method for finding critical points with symmetries, SIAM J. Numer. Anal., 42, 1745, 10.1137/S0036142903431675 Zhou, 2017, Solving multiple solution problems: Computational methods and theory revisited, Commun. Appl. Math. Comput., 31, 1 Gao, 1999, Finding all isolated zeros of polynomial systems via stable volumes, J. Symbolic Comput., 28, 187, 10.1006/jsco.1998.0272 Kelly, 1995 Li, 1999, Solving polynomial systems by polyhedral homotopies, Taiwanese J. Math., 3, 251, 10.11650/twjm/1500407124 Rheinboldt, 1998 Yamamura, 2003, Finding all solutions of nonlinear equations using the simplex method, J. Comput. Appl. Math., 152, 587, 10.1016/S0377-0427(02)00731-8 Nashed, 1993, Convergence of Newton like method for singular operator equations using outer inverse, Numer. Math., 66, 235, 10.1007/BF01385696 Allgower, 1980, Simplicial and continuation methods for approximating fixed points and solutions to systems equations, SIAM Rev., 22, 28, 10.1137/1022003 Allgower, 1989, Large sparse continuation problems, J. Comput. Appl. Math., 26, 3, 10.1016/0377-0427(89)90144-1 Chan, 1982, Arc-length continuation and multi-grid techniques for nonlinear elliptic eigenvalue problems, SIAM J. Sci. Stat. Comput., 3, 173, 10.1137/0903012 Chan, 1984, Techniques for large sparse systems arising from continuation methods Li, 2001, A minimax method for finding multiple critical points and its applications to semilinear PDE, SIAM Sci. Comput., 23, 840, 10.1137/S1064827599365641 Li, 2002, Convergence results of a minimax method for finding multiple critical points, SIAM Sci. Comput., 24, 840 Zhou, 2004, A local min-orthogonal method for finding multiple saddle points, J. Math. Anal. Appl., 291, 66, 10.1016/j.jmaa.2003.10.043 Yi, 2015, An augmented singular transform and its partial Newton method for finding multiple solutions, J. Comput. Appl. Math., 286, 145, 10.1016/j.cam.2015.02.049 Li, 2017, A new augmented singular transform and its partial Newton-correction method for finding more solutions, J. Sci. Comput., 71, 634, 10.1007/s10915-016-0314-6 Nehari, 1960, On a class of nonlinear second-order differential equations, Trans. Amer. Math. Soc., 95, 101, 10.1090/S0002-9947-1960-0111898-8