In Joyce Carol Oates' "The Lady with the Pet Dog," the resolution to the conflict is a weak one (for her character). Anna first decides that she is unhappy with her marriage and her adulterous affair. She concludes that she will never be able to have a life with her lover...
However, by the end of the story, much to her lover's surprise, she is filled with the conviction that she and her lover will live together in something like a "true" marriage. This seems to provide a resolution to her conflict as she searches for happiness and an answer as to which path she should follow in her life: she chooses her lover.
Although this would appear to offer a resolution for Anna's character, the resolution is as solid as a house of cards. Anna and her lover really don't know each other—their connection is more physical. Anna is deciding to go with her lover not because she has made a logical and intelligent decision: she goes with him because she believes that he will make her complete. A woman who was ready to kill herself at one point has rapidly changed her mind, has pulled herself together, and is ready to gamble her future on a man who is nothing as she imagines him to be.
There may well be a resolution, but it is not a healthy one for Anna.