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Is $$e^$$(e^{u}+1)\Delta u+u=0$$ the Euler-Lagrange equation of a functional energy?
Does there exist a functional energy $I$ such that $$e^{u}\Delta u+u=0$$$$(e^{u}+1)\Delta u+u=0$$ is the Euler-Lagrange equation associated with the energy functional $I$?
Is $$e^{u}\Delta u+u=0$$ the Euler-Lagrange equation of a functional energy?
Does there exist a functional energy $I$ such that $$e^{u}\Delta u+u=0$$ is the Euler-Lagrange equation associated with the energy functional $I$?
Is $$(e^{u}+1)\Delta u+u=0$$ the Euler-Lagrange equation of a functional energy?
Does there exist a functional energy $I$ such that $$(e^{u}+1)\Delta u+u=0$$ is the Euler-Lagrange equation associated with the energy functional $I$?
