‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.

 According to a class of constrained‎ ‎minimization problems‎, ‎the Schwartz symmetrization process and the‎ ‎compactness lemma of Strauss‎, ‎we prove that there is a‎ ‎nontrivial ground state solution for a class of $p$-Laplace‎ ‎equations without the Ambrosetti-Rabinowitz condition‎.

according to a class of constrained‎ ‎minimization problems‎, ‎the schwartz symmetrization process and the‎ ‎compactness lemma of strauss‎, ‎we prove that there is a‎ ‎nontrivial ground state solution for a class of $p$-laplace‎ ‎equations without the ambrosetti-rabinowitz condition‎.

This paper deals with the Legendre wavelet (LW) collocation method for the numerical solution of the radial Schrodinger equation for hydrogen atom. Energy eigenvalues for the hydrogen bound system is derived -13.6 eV. Numerical results of the ground state modes of wave function for the hydrogen R(r) or the electron probability density function, has been presented. The numerical results ha...

We establish some general theorems for the existence and nonexistence of ground state solutions of steady-state N coupled nonlinear Schrödinger equations. The sign of coupling constants βij ’s is crucial for the existence of ground state solutions. When all βij ’s are positive and the matrix is positively definite, there exists a ground state solution which is radially symmetric. However, if al...