Your description of the door and the damage do not allow a proper diagnosis here.
More facts are needed.
The Door:
When you say the door is solid wood I think perhaps you mean solidcore.
Solid core doors are typically constructed of three different types of materials:
**1-**a core:two types of material are often used here
a-particleboard(the most common)
**b-**solid wood(laminated like a butcher block,i.e.in thin strips.This is called a “stave core”)
**2-**a solid wood edging around the core
**3-**a thin plywood glued onto each face of the door(This facing is 1/8" thick and is called “doorskin”.)
If you look at the edge of the door you will be able to discern the edge of the doorskin if there is one.
Next,you can determine the core material by looking inside the hole that was cut to insert the lockset.I am refering to the 2 1/8" diameter hole that is located approximately 36"up from the ground.(The doorknob is mounted here)
These pointers will help you better identify the door for those of us who are trying to answer you.
The Damage:
**1-**Did you write that the door was curved vertically?
**2-**Did you mean that the straight board used to determine the curve would be placed on the top and bottom of the door,revealing a gap at waist height or so?
Conditions not Mentioned in your OP:
**1-**Is there an overhanging canopy or roof of any kind?In other words,is the door exposed to rainwater directly?
Some Things to Know About Doors/Wood
**1-**Doors can aquire a lenthwise curve when stored improperly.i.e.leaned at an angle against a wall or something like that.
**2-**Wood will expand when exposed to water,particularly if the water is allowed to linger.
a-Picture a dried out sponge placed in a small puddle of water.As the water is sucked up into the cells,the sponge will grow before you eyes.That happens with wood as well,just not so quickly.
1-The greatest axis of expansion will be across the grain.
**b-**Particleboard will expand a great deal,and having no grain,it will simply expand outward radially from the source of the water.(This weighs rather heavily toward your door being particleboard,since the curve is lengthwise)
**3-**The dry parts will not expand.Dry is a reletive term here,but if one side is dry and the other side is wet,it does demonstrate why the door would curve.
You mentioned that one side gets more sun than the other.This may affect the dry/wet phenomenon that I am referring to.The wet side,because it has expanded,will be the long side,or outside of the curve.See if that’s what is happening.Free movement of air is another very important factor.If one side has stagnant air(encouraging water buildup)and the other side has a moving current of air(drying it out)this too can lend a clue.
I think your door is perhaps unsalvageable,but it’s hard to tell.The suggestions made to turn it around,or plane a curve in the stops are good ones if you decide to keep it.You will definately need to put a marine varnish finish on it at any rate.The stain/sealer type products are never going to offer that level of protection,and that’s what you’ll need.A roof of some kind to protect the top of the door from direct contact with falling rain and dew will help immeasurably as well.This can be as simple as a small board nailed atop the door itself with a pointed shape(like a roof)and a dripcap cut on each edge.
If you you do decide to replace it I hope my points will help you to better preserve your next door.