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We study the set of solutions of the nonlinear elliptic system (P ) ><>: âˆ’âˆ†u + Î»1u = Î¼1u + Î²vu in Î©, âˆ’âˆ†v + Î»2v = Î¼2v + Î²uv in Î©, u, v > 0 in Î©, u = v = 0 on âˆ‚Î©, in a smooth bounded domain Î© âŠ‚ R , N â‰¤â€¦ (More)

- Juncheng Wei, Tobias Weth
- 2007

We consider the nonlinear elliptic system ><>: âˆ’âˆ†u + uâˆ’ u âˆ’ Î²vu = 0 in B, âˆ’âˆ†v + v âˆ’ v âˆ’ Î²uv = 0 in B, u, v > 0 in B, u = v = 0 on âˆ‚B, where N â‰¤ 3 and B âŠ‚ R is the unit ball. We show that, for every Î²â€¦ (More)

We study the fourth order nonlinear critical problem âˆ†u = u âˆ—âˆ’1 in a smooth bounded domain Î© âŠ‚ R, n â‰¥ 5, subject to the boundary conditions u = âˆ†uâˆ’duÎ½ = 0 on âˆ‚Î©. We provide estimates for the range ofâ€¦ (More)

We prove the existence of three nodal solutions of the Dirichlet problem for the singularly perturbed equation âˆ’Îµ u + u = f (u) for Îµ > 0 small on any bounded domain Î© âŠ‚ RN . The nonlinearityf growsâ€¦ (More)

- Andrzej Szulkin, Tobias Weth, Michel Willem
- 2008

This work is devoted to the existence and to qualitative properties of ground state solutions of the Dirchlet problem for the semilinear equation âˆ’âˆ†u âˆ’ Î»u = |u|2âˆ’2u in a bounded domain. Here 2âˆ— isâ€¦ (More)

We consider the 2m-th order elliptic boundary value problem Lu = f(x, u) on a bounded smooth domain Î© âŠ‚ R with Dirichlet boundary conditions u = âˆ‚ âˆ‚Î½ u = . . . = ( âˆ‚ âˆ‚Î½ )u = 0 on âˆ‚Î©. The operator Lâ€¦ (More)

We consider the 2m-th order elliptic boundary value problem Lu = f(x, u) on a bounded smooth domain Î© âŠ‚ R with Dirichlet boundary conditions on âˆ‚Î©. The operator L is a uniformly elliptic linearâ€¦ (More)

- Janosch Rieger, Tobias Weth
- SIAM Journal on Optimization
- 2016

We prove a new multiplicity result for nodal solutions of the Dirichlet problem for the singularly perturbed equation âˆ’Îµ2âˆ†u+u = f(u) for Îµ > 0 small on a bounded domain Î© âŠ‚ RN . The nonlinearity fâ€¦ (More)