In this paper we study a Henon-like equation (see Eq. (1) ), where the nonlinearity f ( t ) is not homogeneous (i.e., it is not a power). By minimization on the Nehari manifold, we prove that for large values of the parameter α there is a breaking of symmetry and non radial solutions appear. This holds for sub- and super-critical growth of the nonlinearity f .

Non radial solutions for a non homogeneous Hénon equation

In this paper we study a H\'enon-like equation (see equations (1) below), where the nonlinearity f(t) is not homogeneous (i.e., it is not a power). By minimization on the Nehari manifold, we prove that for large values of the parameter $\alpha$ there is a breaking of symmetry and non radial solutions appears. This holds for sub- and super-critical growth of the nonlinearity f.

Non radial solutions for non homogeneous H\'enon equation

Scalar curvature type problem on the three dimensional bounded domain

Using bifurcation method, we investigate the existence, nonexistence and multiplicity of positive solutions for the following Dirichlet problem involving mean curvature operator in Minkowski space 

$$\begin{aligned} \left\{ \begin{array}{lll} -\text {div}\left( \frac{\nabla v}{\sqrt{1-\vert \nabla v\vert ^2}}\right) = \lambda f(\vert x\vert ,v) &{}\quad \text {in}\,\, B_R(0),\\ v=0&{}\quad \text {on}\,\, \partial B_R(0). \end{array} \right. \end{aligned}$$

We managed to determine the intervals of the parameter $\lambda $ in which the above problem has zero, one or two positive radial solutions corresponding to sublinear, linear, and superlinear nonlinearities f at zero respectively. We also studied the asymptotic behaviors of positive radial solutions as $\lambda \rightarrow +\infty $.

Bifurcation and positive solutions for problem with mean curvature operator in Minkowski space

http://www.ugr.es/~ecuadif/files/bjtjfa.pdf

Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space

This paper is concerned with ground state solutions for the Henon type equation u(x) =jyj u p 1 (x) in , where = B k (0; 1) B n k (0; 1) R n and x = (y;z)2 R k R n k . We study the existence of cylindrically symmetric and non-cylindrically symmetric ground state solutions for the problem. We also investigate asymptotic behavior of the ground state solution when p tends to the critical exponent 2 = 2n n 2 if n 3.

Existence and asymptotic behavior of solutions for Hénon type equations

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Existence and asymptotic behavior of solutions for Hénon type equations