Main
M. Badiale and E. Serra, Semilinear Elliptic Equations for Beginners - Existence Results via the Variational Approach, Springer-Verlag London, 2011.
T. Cazenave, Semilinear Schrödinger equations, Courant Lecture Notes in Mathematics, American Mathematical Society, Providence, RI, 2003.
M. Willem; Minimax Theorems, Birkhauser Verlag, 1996.
Secondary
A. Ambrosetti, A. Malchiodi, Nonlinear analysis and semilinear elliptic problems. Cambridge Studies in Advanced Mathematics 104. Cambridge University Press, 2007.
D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order, Springer- Verlag, Berlin (Reprint of the 1998 edition), 2001.
M. Struwe, Variational methods. Applications to nonlinear partial differential equations and Hamiltonian systems. Springer-Verlag, Berlin, 1990.
L.C. Evans. Partial differential equations. Second Edition. Providence: American Mathematical Society, 2010.
Q. Han, F. Lin, Elliptic Partial Differential Equations. Courant Lecture Notes 1, American Mathematical Society, 2000.
R. Danchin, P. Raphaël, Solitons, explosion and dispersion - une introduction à l’étude des ondes non linéaires, École Polytechnique, 2015.
T. Tao, Nonlinear dispersive equations: local and global analysis. American Mathematical Society, 2005.
F. Linares, G. Ponce. Introduction to Nonlinear Dispersive Equations, Springer-Verlag, 2015.
A. Haraux, T. Cazenave, An Introduction to Semilinear Evolution Equations. Oxford Lecture Series in Mathematics and Its Applications. 1998.