A degenerate diffusion equation with a nonlinear source term

A critical exponent in a degenerate parabolic equation

“…For q¡p + 1, the assertion is proved in Reference [7], Theorem 4.2, while for q¿p + 1 the proof is nearly identical to that of Lemma 2.1 in Reference [10].…”

Combined Effects of Singular and Superlinear Nonlinearities in Some Singular Boundary Value Problems

“…which implies u 1 ¥ N. There remains only to show that (9) (10) and (11) imply that u 1 is a weak positive solution of (1). The proof is inspired by Lair-Shaker [4].…”

“…We are then interested in the question of whether this solution is unique or not. It is worth mentioning that, in [9,11] the existence of a unique positive solution in the cases when b=1 and 0 < b < 1 (the sub-linear problem) has been proved.…”

Self-Similar Subsolutions and Blowup for Nonlinear Parabolic Equations

“…All nonnegative Ž . solutions exist globally when p -or p s and ⍀ is small enough , w x while they all blow up in finite time if p s and ⍀ is large 11,27,28 . w x On the other hand, local uniqueness can fail for p s s 2 5 , and little seems to be known about local theory when p ) , even for ) 2.…”