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Photosynthesizing plants will have serious troubles and are already well covered by the other answers.

But what about other kinds of plants?

Life is not limited to using the sun as a power source (it just happens to be most abundant one on earth, so most organisms using it easily outcompete others in ecological niches where sunlight is available) - many bacteria can live off hydrogen or other reducible elements (sulfur or elemental metals). Traditionally higher organisms like us humans, but also plants (or fungi) like to cooperate with microorganisms for various reasons.
I see no reason why some plants that evolved on the day side of your planet (and already had the ability to attract bacteria for symbiosis) couldn't have made it to the dark side and once there establish a symbiosis with microorganisms that can extract energy from non-solar sources.

Photosynthesizing plants will have serious troubles and are already well covered by the other answers.

But what about other kinds of plants?

Life is not limited to using the sun as a power source (it just happens to be most abundant one on earth, so most organisms using it easily outcompete others in ecological niches where sunlight is available) - many bacteria can live off hydrogen or other electron rich elements (sulfur or elemental metals). Traditionally higher organisms like us humans, but also plants (or fungi) like to cooperate with microorganisms for various reasons.
I see no reason why some plants that evolved on the day side of your planet (and already had the ability to attract bacteria for symbiosis) couldn't have made it to the dark side and once there establish a symbiosis with microorganisms that can extract energy from non-solar sources.

Photosynthesizing plants will have serious troubles and are already well covered by the other answers.

But what about other kinds of plants?

Life is not limited to using the sun as a power source (it just happens to be most abundant one on earth, so most organisms using it easily outcompete others in ecological niches where sunlight is available) - many bacteria can live off of hydrogen or other reducible elements (sulfur or elemental metals). Traditionally higher organisms like us humans, but also plants (or fungi) like to cooperate with microorganisms for various reasons.
I see no reason why some plants that evolved on the day side of your planet (and already had the ability to attract bacteria for symbiosis) couldn't have made it to the dark side and once there establish a symbiosis with microorganisms that can extract energy from non-solar sources.

Photosynthesizing plants will have serious troubles and are already well covered by the other answers.

But what about other kinds of plants?

Life is not limited to using the sun as a power source (it just happens to be most abundant one on earth, so most organisms using it easily outcompete others in ecological niches where sunlight is available) - many bacteria can live off hydrogen or other reducible elements (sulfur or elemental metals). Traditionally higher organisms like us humans, but also plants (or fungi) like to cooperate with microorganisms for various reasons.
I see no reason why some plants that evolved on the day side of your planet (and already had the ability to attract bacteria for symbiosis) couldn't have made it to the dark side and once there establish a symbiosis with microorganisms that can extract energy from non-solar sources.

Photosynthesizing plants will have serious troubles and are already well covered by the other answers.

But what about other kinds of plants?

Life is not limited to using the sun as a power source (it just happens to be most abundant one on earth, so most organisms using it easily outcompete other in ecological niches where sunlight is available) - many bacteria can life of hydrogen or other reducable elements (sulfur or elemental metals). Traditionally higher organisms like us humans but also plants (or fungi) like to cooperate with microorganisms for various reasons.
I see no reason why some plants that evolved on the day side of your plant (and already had the ability to attract bacteria for symbiosis) shouldn't have made it to the dark side and once there establish a symbiosis with microorganisms that can extract energy from non-solar sources.

Photosynthesizing plants will have serious troubles and are already well covered by the other answers.

But what about other kinds of plants?

Life is not limited to using the sun as a power source (it just happens to be most abundant one on earth, so most organisms using it easily outcompete others in ecological niches where sunlight is available) - many bacteria can live off of hydrogen or other reducible elements (sulfur or elemental metals). Traditionally higher organisms like us humans, but also plants (or fungi) like to cooperate with microorganisms for various reasons.
I see no reason why some plants that evolved on the day side of your planet (and already had the ability to attract bacteria for symbiosis) couldn't have made it to the dark side and once there establish a symbiosis with microorganisms that can extract energy from non-solar sources.