In , we discussed the existence theorem
of weak solutions nonlinear fractional integrodifferential equations in nonreflexive Banach spaces E:
By slightly modifying the proof of Theorem 3, we can apply Lemma 2 to obtain an existence theorem
to (2) when condition (H) is replaced by (G) and either (8) with -1 < [beta] < 0 or (9) with [beta] = 0 is satisfied, which has been established in  for the case [x.sub.0] = 0 when (9) with [beta] = 0 is satisfied and in  for the case [x.sub.0] = 0 when (8) with [beta] = -1 is satisfied.
Wattis, "Existence theorem
for solitary waves on lattices," Communications in Mathematical Physics, vol.
We first utilize the Guo-Krasnosel'skii fixed point theorem to obtain two positive solutions existence theorems
when f grows (p - 1)-superlinearly and (p - 1)-sublinearly with the p-Laplacian, and secondly by using the fixed point index, we obtain a nontrivial solution existence theorem
without the p-Laplacian, but the nonlinearity can allow being sign-changing and unbounded from below.
Ntouyas, "An existence theorem
for fractional hybrid differential inclusions of Hadamard type with Dirichlet boundary conditions," Abstract and Applied Analysis, vol.
Based on the regularity estimates for the semigroups and the classical existence theorem
of global attractors, we prove that the system possesses a global attractor in the space [H.sub.k+1/4] x [H.sub.kk+3/4].
PARK, JKMS 29 (1992) --We apply our existence theorem
to obtain new coincidence, fixed point, and surjectivity theorems, and existence theorems
on critical points for a larger class of multifunctions than upper hemicontinuous ones defined on convex sets.
Even today, Tonelli's theorem remains the central existence theorem
for dynamic problems, although the hypotheses of the theorem can be relaxed: see, for example, .
Lecko, An existence theorem
for a class of infinite systems of integral equations, Math.
It is based on the linearization properties of measure and has many advantages like automatic existence theorem
, converting even the strong no-linear problems into a linear, a known method for determining optimal control as a piece wise constant function.
of a super quasi-Einstein manifold